But Mr. Trump has a singular track record of picking fights with obvious potential running mates like Senator Marco Rubio of Florida, who has indicated a lack of interest in the vice presidency generally and has yet to reconcile with Mr. Trump publicly. Ms. Haley and another potential pick, Gov. Susana Martinez of New Mexico, have sharply criticized Mr. Trump at recent party gatherings and do not want to be associated with his sometimes-angry tone, according to advisers and close associates who have spoken with these Republicans.

Several Republican consultants said their clients were concerned that Mr. Trump’s unusually high unfavorable ratings with all voters and his unpopularity among women and Hispanics could doom him as a general election candidate and damage their own future political prospects if they were on his ticket.

Still, elected officials do have a way of coming around to the vice presidency, and Mr. Trump said in an interview on Saturday that he was in the early stages of mending fences and building deeper relationships with leading Republicans. And in a sign of growing acceptance that Mr. Trump is their likely nominee, several Republicans made it clear that they would join him on the ticket because they think he can win, or because they regard the call to serve as their duty.