Mr. Biden said on Tuesday that it was clear that Mr. Trump would be his opponent in the fall, and he began to court independents and Republicans who dislike the former president — two groups that will most likely be crucial to the president’s hopes in November. And Mr. Trump ramped up his attacks on his lone remaining primary challenger, Nikki Haley, as he sought to portray the nomination as sewn up.

Republican lawmakers began to coalesce around Mr. Trump after his 11-point victory over Ms. Haley on Tuesday, with a number taking to social media to declare the race for the party’s nomination over — “It was never really going to be a contest,” wrote Representative Harriet Hageman, Republican of Wyoming. But the result seemed to underscore Mr. Trump’s potential vulnerabilities: Independent and college-educated voters largely preferred Ms. Haley on Tuesday.

Her refusal to drop out of the race angered Mr. Trump, who spent Tuesday evening attacking her just hours after saying he would not pressure her to bow out. Leading up to the primary, Mr. Trump went from barely mentioning Ms. Haley on the campaign trail to criticizing her at length in his speeches and promoting a racist conspiracy theory that she is not a U.S. citizen.

Ms. Haley was set to return home on Wednesday to South Carolina, where her campaign has already begun placing ads for the primary a month from now, on Feb. 24, and where she was twice elected governor but lags far behind in polls.

Mr. Biden is scheduled to speak on Wednesday afternoon at a conference of the United Auto Workers, which backed him in 2020 but has not yet endorsed a candidate this year.

Here’s what else to know:

• Mr. Biden easily defeated two Democratic challengers — Representative Dean Phillips of Minnesota and the self-help author Marianne Williamson — in New Hampshire despite not being on the ballot. (His supporters ran a write-in campaign on his behalf after he formally boycotted New Hampshire for holding its primary earlier than the Democratic Party had authorized.) Write-in votes are still being processed, but on Wednesday morning his closest competitor, Mr. Phillips, had less than 20 percent of the Democratic vote.

• Mr. Biden is set to send Jennifer O’Malley Dillon and Mike Donilon, two of his top aides in the White House, to take control of his re-election campaign. His current campaign manager, Julie Chávez Rodríguez, is expected to retain her title.

• The turnout in New Hampshire’s Republican primary set a state record, according to a New York Times analysis. The number of voters who cast ballots, which was more than 300,000 as of Wednesday morning, surpassed the state’s previous mark of 296,000 voters, set in the Democrats’ 2020 race, when many supported Senator Bernie Sanders of neighboring Vermont.

• Nevada will host a Republican caucus on Feb. 8, but Ms. Haley is not competing in that contest, instead participating in a Republican primary in the state two days earlier that awards no delegates.