He also said that the election results would bolster his standing going into a highly anticipated meeting with President Xi Jinping of China ahead of the Group of 20 summit in Bali on Monday: “I know I’m coming in stronger, but I don’t need that,” Mr. Biden said.

House Republicans did put forth a platform for governing during the campaign, but it was relatively vague, with most Republican candidates concentrating on criticizing Mr. Biden and Democrats rather than talking about inflation, crime, immigration and other hot-button issues. Republicans also had to contend with Mr. Trump dividing the party and publicly toying with his plans to announce a run for the presidency in 2024.

For Democrats, identifying issues had never been as much of a problem as how to prioritize them: In the days leading up to the election, Mr. Biden and fellow Democrats had struggled with whether to address voter concerns over inflation and the economy, or to stress the threats to abortion rights and even to democracy itself.

The Senate result was the culmination of an intense, final-days campaign push that sought to recast the election on more favorable terms to Democrats — yielding an outcome that has already surpassed many Democrats’ best expectations.

For much of the campaign season, Mr. Biden struggled with low approval ratings and facing a Republican Party whose leaders wanted to make the midterms a referendum on his leadership. He fielded few requests to stump for Democratic incumbents and candidates in purple states. He never campaigned with Ms. Cortez Masto, for example, nor with Senator Mark Kelly of Arizona, who also won a narrow race.

His aides outlined a strategy that centered on showcasing his accomplishments with previous presidents at this stage of their presidencies and contrasting Democratic legislative achievements with Republicans, according to an internal strategy document reviewed by The New York Times. Despite the dearth of campaign requests, they wanted to show that Mr. Biden believes he is a campaigner at heart.

So the president spent time in safer territories, including Oregon, a state that last elected a Republican governor in 1982, to boost Ms. Kotek, the embattled Democratic nominee for governor. Mr. Biden’s schedule picked up in the final weeks, including a cross-country sprint in the last days of the race that took him to New Mexico, California, Illinois, Pennsylvania and New York.