Jane Brady, a Republican National Committee member from Delaware, said Mr. Trump’s pugilistic personality had long been a distraction from his policies, which, generally, much of the party supports.
“Some people look past that, and some people don’t,” she said.
Alex Olson, a Republican strategist, was in Salem, N.H., on behalf of Ron to the Rescue, a new super PAC that is pushing for a 2024 bid by Mr. DeSantis. (The governor and the group are unaffiliated.)
“We have no problem with what Trump has done as president,” Mr. Olson said. “I supported him. But DeSantis can bring together the Chamber of Commerce Republicans and the MAGA Republicans. He is less bombastic, and he understands the legislative process.”
Roland Morasse, 71, of Salem, who had come to see Mr. Trump speak but was angered to find that the event was not for the public — “Shame on them!” he said, adding that “it is only for the elites” — said that he had no problem with Mr. DeSantis, but that he still preferred the former president. “DeSantis would be a good candidate as V.P.,” he said.
Mr. Renacci listed several reasons he wasn’t ready to support Mr. Trump’s presidential bid. The former lawmaker said the party needed “a new face” and also acknowledged that he was stung that Mr. Trump had not done more to help his 2022 primary campaign against Gov. Mike DeWine of Ohio.
“Former President Trump was a great candidate to defeat Hillary Clinton in 2016,” Mr. Renacci said. “But at this stage of the game, we need to look at who the candidates are and see if there is someone who cannot only take us in a new direction but also not split the American people in the process.”
Michael C. Bender reported from Columbia, S.C., and Mei-Ling McNamara from Salem, N.H. Reid J. Epstein contributed reporting from Washington, and Maggie Haberman from New York.