“Part of our research has been why would a conservative Republican voter find this appealing,” Mr. McIntosh said. “A wonkish explanation that trade is actually good for the country probably won’t assuage them.”

In interviews, several savvy and typically confident Republican donors and strategists seemed puzzled about how to topple Mr. Trump, increasingly worried about the feelings he has stirred among the activist base and uneasy about the consequences for the party.

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.