Exit polling from the New Hampshire primary is sending more warning signs that President Trump may struggle to win over a significant portion of the Republican electorate as well as independents ahead of the 2024 election.

In exit polling conducted by CBS News, Mr. Trump struggled with sections of voters who are skeptical of his candidacy in Iowa, moderates, independents, and voters who accept President Biden’s 2020 victory.

Among voters who think that Mr. Biden won the 2020 election legitimately, Ambassador Nikki Haley won 76 percent of the vote to Mr. Trump’s 22 percent. Among voters who do not think Mr. Biden won, 86 percent supported Mr. Trump, and 13 percent supported Ms. Haley.

While Mr. Trump won 71 percent of voters who consider themselves conservatives, 72 percent of voters who consider themselves moderates supported Ms. Haley in the New Hampshire primary.

Likewise, Ms. Haley won 64 percent of Republican primary voters who are registered as independents, compared with 35 percent for Mr. Trump. Mr. Trump won 74 percent of registered Republicans, compared to Ms. Haley’s 24 percent.

A significant portion of voters in the Republican primary, 42 percent, also reported thinking that Mr. Trump would not be fit to be president should he be convicted of a crime. Fifty-four percent said he would be fit.

While Mr. Trump’s strong support among conservatives and Republicans will likely be a winning coalition in the GOP primary — New Hampshire could prove to be Ms. Haley’s most favorable state — weak support among moderates and independents could be a problem for Mr. Trump in the general election.

The managing editor of Sabato’s Crystal Ball at the University of Virginia Center for Politics, Kyle Kondik, notes the potential general election trouble in his analysis of the New Hampshire primary results.

“Dominating with conservatives goes a long way toward winning a party, the Republican Party, that is dominated by conservatives,” Mr. Kondik writes. “But the erosion with moderates may suggest some problems with the general electorate.”

While Mr. Trump spent his victory speech in New Hampshire largely railing against Ms. Haley, who is his last remaining GOP primary opponent, Mr. Biden appeared ready to direct voters’ attention toward the coming rematch between the two presidents.

“It is now clear that Donald Trump will be the Republican nominee,” the president said in a statement. “I want to thank all those who wrote my name in this evening in New Hampshire. It was a historic demonstration of commitment to our democratic process.”

While Mr. Biden’s approval among independents and moderates is also low — he’s at 28 percent among independents and 32 percent among moderates, according to a recent ABC News/Ipsos survey — his campaign is hoping to boost his image among these groups by contrasting him with Mr. Trump.