Asked about those Republicans who seem to be eyeing 2020, a White House spokeswoman, Lindsay Walter, fired a warning shot: “The president is as strong as he’s ever been in Iowa, and every potentially ambitious Republican knows that.”

But in interviews with more than 75 Republicans at every level of the party, elected officials, donors and strategists expressed widespread uncertainty about whether Mr. Trump would be on the ballot in 2020 and little doubt that others in the party are engaged in barely veiled contingency planning.

“They see weakness in this president,” said Senator John McCain, Republican of Arizona. “Look, it’s not a nice business we’re in.”