“Trump is emotionally, intellectually and psychologically unfit for office, and I’m sure a lot of Republicans feel the same way,” Mr. Trott said. “But if they say that, the social media barrage will be overwhelming.” He added that he would be open to the presidential candidacy of former Mayor Michael R. Bloomberg of New York.

On the other hand, Mr. Trump dangles rewards to those who show loyalty — a favorable tweet, or a presidential visit to their state — and his heavy hand has assured victory for a number of Republican candidates in their primaries. That includes Gov. Ron DeSantis of Florida, who did as many Fox News appearances as possible to draw the president’s attention.

“The greatest fear any member of Congress has these days is losing a primary,” said former Representative Carlos Curbelo, Republican of Florida, who lost his general election last year in a heavily Hispanic Miami-area district. “That’s the foremost motivator.”

The larger challenge with Mr. Trump is that all politics is personal with him, and he carefully tracks who on television is praising him or denouncing his latest rhetorical excess. “He is the White House political director,” Scott Reed, a longtime Republican consultant, said.

More conventional presidents may be more understanding of lawmakers who are pulled in a different direction by the political demands of their districts — but Mr. Trump has shown little tolerance for such dissent. Mr. Curbelo, for instance, occasionally spoke out against Mr. Trump, particularly over immigration policy, and the president took notice.

Riding with Mr. Trump in his limousine on Key West last year, Mr. Curbelo recalled in an interview that the president had noted that people were lining the streets to show their support for him, and asked Mr. Curbelo if they were in his district.

He said they were, prompting the president to turn to others in the car and say: “Maybe Carlos will stop saying such nasty things about me,” Mr. Curbelo recalled.