Spurred by Donald J. Trump’s mounting victories, a small but influential — and growing — group of conservative leaders are calling for a third-party option to spare voters a wrenching general election choice between a Republican they consider completely unacceptable and Hillary Clinton.

While he has gained intense popularity on the right, Mr. Trump has alienated key blocs in the Republican coalition with his slash-and-burn campaign. For many, his initial refusal last weekend to disavow an endorsement from David Duke, the white supremacist, was a breaking point.

Two top Republicans, Senator Ben Sasse of Nebraska and Gov. Charlie Baker of Massachusetts, said this week that they would not vote for Mr. Trump in November.

Mr. Trump has alienated voters from several wings of the party: mainstream Christian activists, who view his angry outlook as antithetical to their faith; centrists, who see him as the most divisive politician in a generation; and national security experts, who have recoiled from his praise for autocrats like President Vladimir V. Putin of Russia and believe he should not control nuclear weapons.