Andy Sabin, a New York supporter of Jeb Bush, said the question of what to do about Mr. Trump had come up repeatedly on the Hamptons fund-raising circuit this summer, as what seemed like a summer romance by disenchanted conservatives blossomed into a full-blown insurgency.

“He’s been a topic, and he obviously disgusts a lot of people, because he’s been vile,” said Mr. Sabin, who is also a donor to American Crossroads, the party’s leading super PAC. “But he’s also been able to bring out what people feel about their government.”

The cost of an anti-Trump campaign would be daunting: Reshaping opinions about Mr. Trump, a candidate with universal name recognition and a knack for garnering free airtime and column inches, could cost as much as $20 million. A sustained campaign aimed at Fox News viewers could cost $2 million a week, one Republican consultant working for a rival candidate estimated, while a more targeted effort, aimed at Iowa caucus-goers later this fall, would require as much as $10 million.

And there is no certainty of success: A group identified with the Republican establishment would risk ending up in a war with Mr. Trump, while a new group — such as a political nonprofit to which other donors and organizations could secretly funnel cash — would play into Mr. Trump’s comments about lobbyists and corporations scheming to prop up his rivals. Mr. Trump also has begun to preview such attacks.