Governor DeSantis has whipsawed his way through the national conversation this month, first by putting migrants on planes or buses to Democratic strongholds and then shifting to a more traditional role of crisis manager as one of the strongest hurricanes to ever hit America barreled into his state.

Facing a reelection in November that could be a precursor to a presidential campaign, the approach has been awkward at points. Navigating one of his state’s darkest moments, Mr. DeSantis, a Republican, must partner with a Democratic president he has spent the better part of two years criticizing.

He’s also accepting the type of federal disaster aid and assistance he rejected as wasteful while he was a member of Congress.

But together, the developments over the past two weeks offer insight into how Mr. DeSantis might govern if he wins another term as governor or advances in a 2024 presidential contest.

He’s willing to use — and potentially exceed — the raw executive power of his office to pick at America’s most sensitive divides on issues like immigration. In a sudden moment of disaster, however, he’s capable of striking a more unifying tone in a way that President Trump — once a close ally and now a potential 2024 rival — rarely demonstrated.

“At the end of the day, I view this as something that you’ve got folks that are in need, and local, federal and state, we have a need to work together,” Mr. DeSantis said at a briefing late Thursday, taking a far more conciliatory tone toward an administration he bitterly criticized just days earlier. He expressed appreciation that FEMA has approved every request for aid he has made, and said he welcomed the agency’s director to travel with him to view destruction.

The shift in tone could prove temporary. When a 12-story condo building in Surfside, Florida, collapsed last year and killed 98 people, Mr. DeSantis appeared with local officials, including Democrats who praised his assistance. He sat next to President Biden during a briefing with first responders and local officials in Miami. Within months, however, he returned to partisan brawls.

Facing another disaster, Mr. DeSantis didn’t answer questions this week about whether he would meet with Mr. Biden, saying he wasn’t sure about the president’s travel plans. At a FEMA briefing on Thursday, Mr. Biden also aimed to set aside hostilities, saying he would visit Florida when conditions allow and meet with Mr. DeSantis “if he wants to meet.”

Messrs. Biden and DeSantis both said they have spoken more than once. And at Mr. DeSantis’ request, Mr. Biden on Thursday declared a major disaster in parts of Florida, freeing up additional federal assistance to state and local governments and individuals.

“We’re going to build it back with the state and local government,” Mr. Biden said.

The White House press secretary, Karine Jean Pierre, tweeted that Messrs. Biden and DeSantis spoke again by phone on Friday, as the FEMA administrator is on the ground in Florida.

Mr. DeSantis’ embrace of federal help is a shift from his early days as a congressman, when he voted against a federal relief package for New York and New Jersey after Hurricane Sandy. That drew criticism this week from some New York-area officials and other Democrats who described the turnaround as a move from cruel to hypocritical.

A University of Florida political science professor, Richard Conley, said Mr. DeSantis is doing what he needs to do, pragmatically and politically. While Mr. DeSantis is popular in the reliably Republican area of southwest Florida that was hardest hit by Hurricane Ian, he said people will inevitably become frustrated if it takes too long to get help, and will look for someone to blame.

“He’s just got to get the job done,” said Mr. Conley. “The question will be: Going forward, does he look very statesmanlike? Does this help him with an eventual 2024 run? I don’t know, it remains to be seen.”

Since his early years running for governor, Mr. DeSantis has been linked to Mr. Trump. Mr. DeSantis was a relatively obscure third-term congressman when he announced his 2018 bid for governor — and a Trump endorsement — on Fox News. He echoed some of Mr. Trump’s favorite lines as he campaigned, pledging, for example, to “drain the swamp” in Tallahassee. Mr. Trump took credit for the victory, though their relationship is said to have chilled amid the 2024 talk.

As governor, Mr. DeSantis has elevated issues that excite the conservative base and used his resources and the power of his office to get things done his way, pushing the limits of his legal authority.

During the COVID pandemic, Mr. DeSantis insisted Florida would remain open. He shunned guidance from federal health experts and once said of Dr. Anthony Fauci that someone should “chuck him across the Potomac.” He also stripped funding from school districts that implemented mask mandates.

This spring, Mr. DeSantis signed legislation stripping Disney of a special agreement that allowed the theme park to govern itself, after the company criticized a new state law that put limits on discussions of sexuality in public schools.

Mr. DeSantis also suspended an elected Democratic prosecutor in Tampa from office over statements about not pursuing criminal charges in abortion, transgender rights and certain low-level cases. The prosecutor has since filed a federal free speech lawsuit against the governor.

In recent weeks, Florida under Mr. DeSantis’ direction paid for two flights of migrants from Texas to Martha’s Vineyard. Mr. DeSantis was the latest GOP governor, frustrated over the federal government’s response to policing the southern border, to transport the migrants to Democratic cities.

Mr. DeSantis defended the move as a way to make immigration a “front-burner issue” ahead of the midterms. Critics questioned the legality, and his Democratic opponent for governor said it represented a new low level of shrewdness.

“It’s amazing to me what he’s willing to do for sheer political gain,” his gubernatorial challenger, the former governor, Charlie Crist, said.

Mr. Conley, who wrote a book about Mr. Trump and populism, said he understands the comparisons between the two men, both often provocative Republicans. But he noted key differences, including that Mr. DeSantis is more disciplined and restrained with statements on social media.

“He may say controversial things, but I don’t think he’s going to sit around at 3 or 4 in the morning and contemplate how to get back at Mitch McConnell or something” as Mr. Trump would do, Mr. Conley said.

Mr. Trump also drew criticism for his responses to natural disasters, which often failed to convey empathy.

After Puerto Rico was flattened by Hurricane Maria, he flew to San Juan and threw paper towels into the crowd, withheld aid and questioned whether a death toll in the thousands was contrived by Democrats to make him look bad. 

On a trip to Houston after Hurricane Harvey, he was criticized for not meeting with storm victims. When he returned days later, Mr. Trump urged those at a shelter to “have a good time.”

Natural disasters have historically put American politicians in predicaments.

Years earlier, President George W. Bush left the impression of overlooking Hurricane Karina’s devastation in New Orleans when he flew over the city while returning to Washington from vacation. He later praised the FEMA director, Michael Brown, as doing “a heck of a job.”

New Jersey’s Republican governor, Chris Christie, a Republican, and President Obama felt political effects of a friendly greeting after Hurricane Sandy. The image may have helped Mr. Obama project a moderate, bipartisan front days before his election for a second term but conservatives derided Mr. Christie for what they called a “hug.”

At Thursday’s afternoon briefing, Mr. DeSantis spoke of surveying the damage, from a wiped out causeway between the mainland and Sanibel Island off Fort Myers to destroyed homes and hundreds of people rescued.

“These are resilient folks,” he said. “They will bounce back, but we just want to make sure that we can kind of pave the way for them.”