When Representative Troy Nehls of Texas voted last year to reject Donald J. Trump’s electoral defeat, many of his constituents back home in Fort Bend County were thrilled.

Like the former president, they have been unhappy with the changes unfolding around them. Crime and sprawl from Houston, the big city next door, have been spilling over into their once bucolic towns. (“Build a wall,” Mr. Nehls likes to say, and make Houston pay.) The county in recent years has become one of the nation’s most diverse, where the former white majority has fallen to just 30 percent of the population.

Don Demel, a 61-year-old salesman who turned out last month to pick up a signed copy of a book by Mr. Nehls about the supposedly stolen election, said his parents had raised him “colorblind.” But the reason for the discontent was clear: Other white people in Fort Bend “did not like certain people coming here,” he said. “It’s race. They are old-school.”

A shrinking white share of the population is a hallmark of the congressional districts held by the House Republicans who voted to challenge Mr. Trump’s defeat, a New York Times analysis found — a pattern political scientists say shows how white fear of losing status shaped the movement to keep him in power.

The portion of white residents dropped about 35 percent more over the last three decades in those districts than in territory represented by other Republicans, the analysis found, and constituents also lagged behind in income and education. Rates of so-called deaths of despair, such as suicide, drug overdose and alcohol-related liver failure, were notably higher as well.

Although overshadowed by the assault on the Capitol on Jan. 6, 2021, the House vote that day was the most consequential of Mr. Trump’s ploys to overturn the election. It cast doubt on the central ritual of American democracy, galvanized the party’s grass roots around the myth of a stolen victory and set a precedent that legal experts — and some Republican lawmakers — warn could perpetually embroil Congress in choosing a president.

To understand the social forces converging in that historic vote — objecting to the Electoral College count — The Times examined the constituencies of the lawmakers who joined the effort, analyzing census and other data from congressional districts and interviewing scores of residents and local officials. The Times previously revealed the back-room maneuvers inside the House, including convincing lawmakers that they could reject the results without explicitly endorsing Mr. Trump’s outlandish fraud claims.

Many of the 139 objectors, including Mr. Nehls, said they were driven in part by the demands of their voters. “You sent me to Congress to fight for President Trump and election integrity,” Mr. Nehls wrote in a tweet on Jan. 5, 2021, “and that’s exactly what I am doing.” At a Republican caucus meeting a few days later, Representative Bill Johnson, from an Ohio district stretching into Appalachia, told colleagues that his constituents would “go ballistic” with “raging fire” if he broke with Mr. Trump, according to a recording.

Certain districts primarily reflect either the racial or socioeconomic characteristics. But the typical objector district shows both — a fact demographers said was striking.

Because they are more vulnerable, disadvantaged or less educated white voters can feel especially endangered by the trend toward a minority majority, said Ashley Jardina, a political scientist at George Mason University who studies the attitudes of those voters.

“A lot of white Americans who are really threatened are willing to reject democratic norms,” she said, “because they see it as a way to protect their status.”

That may help explain why the dispute over Mr. Trump’s defeat has emerged at this moment in history, with economic inequality reaching new heights and the white population of the United States expected within about two decades to lose its majority.

Many of the objectors’ districts started with a significantly larger Black minority, or had a rapid increase in the Hispanic population, making the decline in the white population more pronounced.

Of the 12 Republican-held districts that swung to minority white — almost all in California and Texas — 10 were represented by objectors. The most significant drops occurred in the Dallas-Fort Worth suburbs and California desert towns, where the white percentage fell by more than a third.

Lawmakers who objected were also overrepresented among the 70 Republican-held districts with the lowest percentages of college graduates. In one case — the southeast Kentucky district of Hal Rogers, currently the longest-serving House member — about 14 percent of residents had four-year degrees, less than half the average in the districts of Republicans who accepted the election results.

While Mr. Nehls’s district exemplifies demographic change, Representative H. Morgan Griffith’s in southwest Virginia is among the poorest in the country. Once dominated by coal, manufacturing and tobacco, the area’s economic base eroded with competition from new energy sources and foreign importers. Doctors prescribed opioids to injured laborers and an epidemic of addiction soon followed.

Residents, roughly 90 percent of them white, gripe that the educated elites of the Northern Virginia suburbs think that “the state stops at Roanoke.” They take umbrage at what they consider condescension from outsiders who view their communities as poverty-stricken, and they bemoan “Ph.D pollution” from the big local university, Virginia Tech. After a long history of broken government promises, many said in interviews they had lost faith in the political process and public institutions — in almost everyone but Mr. Trump, who they said championed their cause.

Marie March, a restaurant owner in the town of Christiansburg, said she embodied “the mind-set of the Trump MAGA voter.”

“You feel like you’re the underdog and you don’t get a fair shake, so you look for people that are going to shake it up,” she said of the local support for Mr. Trump’s dispute of the election results. “We don’t feel like we’ve had a voice.”

Ms. March, who said she attended the Jan. 6 rally in Washington but did not go to the Capitol, was inspired by Mr. Trump to win a seat in the state legislature last year. She said she could drive 225 miles east from the Kentucky border and see only Trump signs. No one in the region could imagine that he received fewer votes than President Biden, she insisted.

“You could call it an echo chamber of our beliefs,” she added, “but that’s a pretty big landmass to be an echo chamber.”

For America or Against It

In a bustling clinic called the Health Wagon in Mr. Griffith’s district, Paula Hill-Collins sees low-income and uninsured patients with maladies from tooth decay to heart conditions and diabetes.

Since the last election, they have often raised another complaint: the false claim that Democrats stole Mr. Trump’s victory.

“‘Did you see that box of votes that was thrown away? Did you see they found extra ones?’ This is what we hear from our patients,” said Ms. Hill-Collins, a nurse practitioner who grew up in the town of Coeburn, population 1,600.

Residents of the area — former coal towns at the southern end of Appalachia — have felt cheated for generations, she said. “They believe it because look what’s happened to us,” she said, recalling the exploitation of her community first by mining interests and more recently by drugmakers. “That’s fed a culture of suspicion.”

Families still swap stories about underhanded land deals that prospectors struck with residents more than a century ago for minerals under the hills. Now, the number of coal miners has plunged to less than 2,000 from more than 10,000 employed at about 340 mines three decades ago, according to government statistics.

In a congressional district bigger than New Jersey, villages that once hummed with the sounds of children now feel “just like ghost towns,” said Betty S. Hess, 75, of Honaker, population 1,200. A daughter, sister and wife of miners, she now helps lead an association to support those with black lung disease.

Nearly a fifth of the homes in the district sit empty. The average household earns about $46,000 a year, about a quarter less than in other Republican-held districts. Even with Virginia Tech, only about 21 percent of the residents hold college degrees, compared with about 31 percent nationally.

The toll of the opioid crisis is unmistakable. In Lebanon, population 3,100, seven addiction clinics line Main Street. Kimberly Harris, 50, director of a nearby funeral home, said she typically buried at least one overdose victim a month. “The older I get, the younger they get,” she said, noting that she adopted the child of a relative who had become addicted. (Last week, she was preparing a service for a 67-year-old who had died of lung cancer after working in coal mines from the age of 14.)

Conditions like diabetes and heart disease overlap so often that health workers feel lucky when their patients can walk in the door, said Teresa Owens Tyson, a nurse practitioner at the Health Wagon. “Sometimes they collapse in the parking lot,” she said.

Although not all are so hard-pressed, the districts of the House objectors share similar disadvantages. Households there had nearly 10 percent less annual income in 2020 than those in other Republican areas. Not only were college degrees less common, so were high school diplomas.

The G.O.P.’s hold on those districts reflects its shift away from its former country club image to become the party of those left behind. The residents of Democratic districts, on average, are better educated and earn significantly more.

Tim Wilson, a 60-year-old Army veteran who owns a business in Christiansburg that provides wigs and other supplies to cancer patients, said he won a town council seat last year to help attract business and jobs.

Yet he feared the cultural cost of outside investment. A big employer “would also bring with it all the executives and what comes with it from Northern Virginia or California, one of the strong blue regions,” he said. “There is this fear.”

The same distrust drove feelings about the last election, he said: Democratic elites in the big cities — the ones who took people “from being coal miners to being put out on the street” — were pushing what he called the myth that the election had run perfectly.

“If we don’t show the people that are a level above us and a level above them in elected offices that we mean business, it’ll never change anything,” he said. “We need to show them that we have the courage to stand up to the status quo.”

Others took offense at the suggestion that election doubts were tied to income, education or faith. (Districts of objectors had higher concentrations of evangelical Protestants than other Republican-held areas, according to the most recent data available.)

Instead, some residents said that their reasons for questioning the results should be obvious to anyone: the relatively small size of Mr. Biden’s rallies, the overnight disappearance of Mr. Trump’s early lead as more votes were tallied, the allegations about stuffed ballot drop boxes.

“It’s not a political thing. It’s a we-love-our-country thing,’” said Alecia Vaught, 46, a homemaker and Republican organizer in Christiansburg. “You’re either for America or you’re not.”

Vanishing Opportunities

Mr. Griffith, 64, a lawyer and state legislator before joining Congress, built his career fighting for the lost cause of coal. In the Tea Party wave of 2010, he defeated a 14-term Democratic incumbent by slamming him for supporting carbon caps.

His commitment to fossil fuels has made Mr. Griffith a vocal critic of electric cars, which he notes cannot yet cross his district without recharging. Earlier this year, he criticized Democrats for holding a hearing on the technology even though many Americans were worried about high energy prices because the Russian war in Ukraine had cut global oil and gas supplies.

“Have my friends forgotten where our electricity comes from today?” he asked fellow lawmakers, arguing for focusing on U.S. production of coal, oil and gas.

He was an enthusiastic backer of Mr. Trump, who had made a campaign promise to bring coal jobs back. After he took office, Mr. Griffith celebrated: “The war on coal is over.”

When Mr. Trump lost in 2020, his claims of a stolen election quickly took hold in the district. “I’d be pumping gas and people who didn’t even know me would want to know if I thought the election was stolen,” said Frank Kilgore, 70, a lawyer-lobbyist and local historian who is an independent.

“Morgan heard it more and more from his base,” Mr. Kilgore added. Local Republican leaders “said they thought it was stolen, too,” raising the specter of a primary challenge if Mr. Griffith voted to accept the results. Constituents circulated a petition demanding that he fight Mr. Trump’s loss.

Yet Mr. Griffith was not among the vocal chorus of House Republicans echoing Mr. Trump. On Jan. 6, 2021, he voted to object citing only changes to election procedures during the pandemic.

The congressman, who declined to comment for this article, wrote to constituents after Mr. Biden was inaugurated: “It is time to move forward.”

But local party leaders have not given up.

In Montgomery County, the largest in the district, the party has been offering weekly screenings since the summer of the film “2000 Mules.” Using faulty arguments, the film alleges that Democrats conspired to stuff ballot drop boxes to engineer Mr. Trump’s defeat.

“The other side always talks about facts, facts, facts, but facts change and facts are whatever you want them to be,” said Jo Anne Price, 70, host of the screenings, accusing news organizations of distorting the truth.

The screenings take place at a strip mall in Christiansburg, where she also leads seminars on accounting, cursive and “the foundation of the nation.” A biracial woman who traces her lineage to enslaved people and the white family that owned them, Ms. Price sells and flies the Confederate flag. “I’m proud of all the things that made my country what it is,” she said.

She became involved in local politics during the pandemic, organizing protests against masks and vaccines. This year she replaced the county party’s chair, faulting her predecessor for not pushing the “stop the steal” cause.

At a recent meeting, Ms. Price warned fellow party volunteers that thousands of former Virginia Tech students may be registered to vote in her county. Her group vowed to seek new laws to purge voter rolls and to elect pro-Trump insurgents.

“We’re going to set this county on fire,” Ms. Price promised.

A New America

Less than a month before the 2020 election, Democrats organized a rally outside a predominantly Black high school in a Fort Bend town adjacent to Houston, and a caravan of Trump backers showed up.

Several arrived in military vehicles. One drove a white hearse displaying a sign: “Collecting Democratic Votes One Dead Stiff at a Time.” A placard on the windshield served as a rejoinder to the recent racial justice movement: “All Lives Matter.” A mannequin that appeared to be a Black woman lay in an open coffin.

Eugene Howard, 39, an alumnus of the high school and then president of a local chapter of the N.A.A.C.P., said Trump supporters shoved him and used a racist slur as he walked to his car.

“The goal was intimidation,” he argued in an interview, saying it was motivated by the same emotions as the denial of the 2020 election results: “white fear and backlash.”

Texas is one of six states where the white population is now outnumbered by Black, Hispanic and Asian residents. Mr. Nehls’s district, which includes most of Fort Bend County, is part of the reason: It swung from nearly 70 percent to less than 40 percent white over the last three decades.

But changing demographics in many places may not yet be reflected at the polls, because of a larger white share of the voting-age population and higher turnout levels. Exit polls show that white Texans still made up 60 percent of the state’s voters in 2020.

The greater Houston area is the center of the state’s transformation and also a hub of the “stop the steal” movement. True the Vote, the organization behind some of the loudest accusations of voter fraud, was founded 12 years ago by a Fort Bend resident who claimed that a nonprofit was falsely registering voters in Black and Hispanic neighborhoods in Houston. A cluster of congressmen who actively promoted Mr. Trump’s election denial come from the area. Next month, another Republican who calls the election stolen is expected to replace an incumbent who accepted the Biden victory and did not seek re-election.

Many Fort Bend-area Republicans say their doubts about the 2020 results have nothing to do with race.

“I think it has more to do with polarization than it does with racial or demographic issues,” said Jacey Jetton, 39, a Texas state legislator and former G.O.P. county chairman. “We are so divided now,” he added, that no one can accept that their opponents “believe what they believe.”

He said he “declined to speculate” whether Mr. Trump had won or lost in 2020. But Mr. Jetton, who is Korean American, noted that forward-looking Republicans in many places were competing for minority voters. In Fort Bend, the party won local races through 2016, partly through outreach to Black, Hispanic and immigrant groups — particularly Asian Americans. The county government flipped to the Democrats under Mr. Trump in 2018, organizers in both parties said, in part because the president’s rhetoric — “shithole countries,” a “Muslim ban” — had repelled those voters.

But William Thompson, 47, a white Republican who declined to seek re-election in 2020 as a Fort Bend town constable, said the racial shift in the electorate helped explain the denial of Mr. Trump’s defeat.

“The Republican Party is, you know, dominated by white males, and the hard-core Republicans — especially in a place like Fort Bend — might not be fully awake to the fact that we are a melting pot,” he said. “They just may not believe that all these people of color — all these different religions, maybe Muslims, maybe atheists — have moved in and are voting.”

Craig LeTulle, 65, a building contractor who described himself as dubious about Mr. Biden’s win, felt similarly.

Mr. LeTulle used to lead the county party’s outreach to minority voters,courting culturally conservative Asian American business owners and professionals. He said he often visited the local Hindu temple in his cowboy hat and boots with a kurta over his Wranglers. And he cited some success, like persuading a Black Democrat who had lost her primary to switch parties.

“You could see the demographic changes coming a long time ago,” he said, “but if you look at a picture of our list of candidates, it is white, white, white, white, white.”

Right-leaning media commentators sometimes assert that liberals are conspiring to increase the number of nonwhite voters in order to “replace” white ones. That theory may have particular traction in objectors’ districts, where the white share of the population fell an average of 14 percent over the last three decades, compared with about 10 percent in other Republican-held areas.

Many objector districts are in former Confederate states that were home to large Black populations. Black residents make up about 20 percent of Fort Bend, including descendants of former slaves who once worked on a sugar plantation, the site of what is now the town of Sugar Land.

The town is the center of the fast-growing Asian American population, now a fifth of the county. The largest mosque, Maryam Islamic Center, is so besieged by candidates of both parties that it limits political speeches to three Fridays each election cycle and caps them at three minutes.

A sprawling Hindu temple with a specialized grocery store and cafe draws visitors from across the South and Southwest. And where football once ruled, cricket leagues flourish. About a dozen pitches around the county attract players with roots in former British colonies — despite occasional friction with neighbors.

In some farm towns, “they don’t want us going into their property after a ball — some guys say they will shoot if we trespass,” said Devon Small, 68, a Jamaican-born umpire. “But some of the neighbors are friendly and they will come and ask, what is that?”

Mr. Nehls called immigrants an asset to the community.

“If you go to the Sugar Land memorial hospital and try to read the names of the doctors, we can’t pronounce them or spell them, right?” the congressman said in an interview at his book signing.

“But those are the same guys who are going to be putting in my stent in a few years!” he continued, trying to sound out the name of his own cardiologist from a business card. “I think he is from Pakistan, and I think he is a Muslim,” Mr. Nehls said, “and I love him!”

‘Power Grab’

Some Fort Bend Democrats said they saw an obvious connection between the declining white share of the population and the refusal by Mr. Nehls and his supporters to accept Mr. Trump’s defeat.

“It is a power grab by white Republicans,” said K.P. George, a Democrat born in India who was elected in 2018 as the county’s top executive, the first nonwhite person to hold the office.

Xenophobic hostility “is all I get,” he quipped in an interview.

Mr. George has cited slurs against him posted by online accounts backing his Republican opponent this fall. These have included falsehoods that he is a Muslim and changed his name “to sound more American,” attempts to link him with Osama bin Laden and a demand that he recognize a “white heritage month.”

In response, his rival has accused Mr. George and other Democrats of stoking “racial division to distract from their failures of leadership.” (That candidate is Mr. Nehls’s twin brother, Trever, a former elected constable and ex-Army colonel. He declined to comment.)

Troy Nehls, a veteran of the wars in Iraq and Afghanistan, served as the county sheriff for eight years before running for Congress in 2020. His seat appears safe this year because the Republican-controlled state legislature redrew the boundaries of his district to include more predominantly white and solidly Republican terrain outside Fort Bend County. Whites now make up a majority of the eligible voters in the district.

Fort Bend Republicans say they are playing down election integrity issues in the midterms, wary that attention on Mr. Trump’s dispute may turn off independent voters worried about everyday matters like inflation. Still, Bobby Eberle, the county party chairman, said fears of voter fraud after the last election drove many of the calls he received from volunteers.

The Harris County Republican Party is training poll watchers to suspect mischief from local election workers. “There was a lot more shenanigans going on than I was aware of,” said Jacqueline Clinton, 55, leaving one of the training sessions in Kingwood, a Houston suburb.

For his part, Mr. Nehls said election fraud was the only thing that could stop “the greatest leader of my lifetime” from returning to the Oval Office in 2024.

“In a fair election, you can’t beat Donald Trump!” Mr. Nehls said, posing for photographs in front of a life-size photo of the former president.

He saw no fear of demographic change among his supporters, he said. “These people aren’t against brown or Black people. They just don’t like the way Democrats are running the country.”

Steve Eder contributed reporting. Julie Tate contributed research. Data analysis was contributed by Andrew Beveridge and Susan Weber-Stoger of SocialExplorer.com. Produced by Hang Do Thi Duc and Rumsey Taylor.

Methodology: The Times relied on several data sources to evaluate differences in congressional districts represented by lawmakers who did or did not object to the 2020 election results.

Measurements of demographics, income and education were computed using data from the long-form census of 1990 and the American Community Survey’s five-year estimates for 2020.

To compare the same congressional districts reliably across years, the analysis first tagged a set of census tracts corresponding to their boundaries in the current Congress. Data from 1990 for each tract was then aggregated to create district equivalents.

The analysis measured the differences between groups of lawmakers using median district values. Income values are a weighted average of the tract medians. For racial comparisons, “white” refers to the white non-Hispanic population.

Age-adjusted mortality was based on C.D.C. data. The agency suppresses counts when fewer than 10 deaths occurred in a county in a given time period. We imputed suppressed values by choosing a random integer between one and five, a range chosen in consultation with academic researchers. When county data was listed as “missing,” the county’s population was excluded from the rate calculation. County data was allocated to congressional districts using population figures from the Missouri Census Data Center.

Religious affiliations were estimated using the 2010 U.S. Religion Census, conducted by the Association of Statisticians of American Religious Bodies, the most recent version available.

In determining which Republican lawmakers were included in the group that did not object, the analysis excluded eight lawmakers who were absent from voting on Jan. 6, 2021.