Even as Governor DeSantis surges in polls pitting him against President Trump in the 2024 Republican presidential primary, his Democratic gubernatorial challenger, Congressman Charlie Crist — a former governor himself — looks poised to give Mr. DeSantis a run for his money this fall in Florida.

The most recent data suggest Mr. DeSantis is at risk of repeating history: In 1994 another conservative rising star, Jeb Bush, saw his momentum toward the Republican presidential nomination halted when he lost the Florida gubernatorial race.

Early polling on the 2024 presidential primaries suggest Mr. DeSantis is beginning to pull ahead of Mr. Trump. A McLaughlin and Associates national poll released Friday showed Mr. DeSantis is the preferred presidential candidate of about 32 percent of Republicans compared to Mr. Trump’s 17 percent.

“Trump slipping in pre-primary polls is part of a typical pattern,” the director of the University of New Hampshire Survey Center, Andrew Smith, said. “A party’s losing candidate in the prior election is typically the best-known person in their party.”

Polling in New Hampshire, a key early voting state, put Mr. DeSantis ahead of Mr. Trump as well: The Florida governor has 39 percent support to 37 percent for Mr. Trump among state Republicans, a recent University of New Hampshire poll shows.

“As the primary gets closer, new candidates emerge and attract more media attention, and therefore more voter attention, than the losing candidate from the previous election,” Mr. Smith said.

The New Hampshire numbers are a complete turnaround from a year ago, when Mr. Trump enjoyed a nearly  30-point lead. They also demonstrate Mr. DeSantis’s growing prominence on the national stage.

A professor of political science at John Jay College of Criminal Justice, Brian Arbour, tells the Sun that Mr. DeSantis’s record as governor appears to be a boon for him electorally.

“Between polarization and the national trend, Republicans are slight favorites in just about every swing-state race,” he said. “They’ve got some candidates I’m skeptical of, but DeSantis has a much better track record than some of the rest of them.”

So far, Mr. DeSantis’s national prominence isn’t helping him much at home. The latest nonpartisan polling, conducted by the Political Matrix/the Listener Group in Florida, shows Mr. Crist up by about a point against Mr. DeSantis in a general election faceoff.

Although that election is still months away, the results line up with what Mr. Arbour said he would expect: that voters are slightly favoring Mr. Crist rather than straddling the fence.

“The biggest thing to look for would be, ‘Do the numbers for the Democrat go up?’” Mr. Arbour said. “If the undecideds are increasing, I think that’s soft DeSantis supporters and he should be able to get them back.”

Mr. Arbour argues that some of the sagging support for Mr. DeSantis in Florida could be tied to his presidential aspirations, though he urges caution in hastily declaring Mr. Crist the frontrunner.

“While there does seem to be some dislike for a governor or congressman facing more nationally than they do in their district or state, my guess is that it’s unlikely to hurt him that much in the end,” he said.

Mr. DeSantis’s situation is reminiscent that of Mr. Bush in 1994, when Governor Chiles narrowly beat him. Mr Bush did go on to win another race for governor, in 1998, but his potential 1996 presidential bid was quashed.

Although Mr. Bush has pushed back on the notion, many said at the time that he was the natural heir to the political legacy of his father, President George H. W. Bush.

If the latest polling from Florida holds, Mr. DeSantis could find himself in the same situation as the younger Mr. Bush.

The University of Virginia’s Center for Politics rates Florida as a “likely Republican” win in the 2022 gubernatorial race, a characterization that Mr. Arbour ultimately agrees with.

“He’s in a swing state that’s more favorable to Republicans than the rest,” he said, noting national trends on voter enthusiasm. “Republicans are going to be more likely to vote than Democrats.”