“Goodbye @GOP,” Mr. Howe wrote, adding: “I’m drinking wine directly out of the bottle right now. #NeverTrump.”

Steve Deace, a conservative radio show host in Iowa, said he would never waver from his pledge to oppose Mr. Trump to the end.

“You can sign my name in blood,” he wrote on Twitter.

As Republicans raced to social media to declare their unshakable opposition to Mr. Trump, some expressed hope that a national movement might still arise to stop him; others alluded to the harsh judgments of history and said they wanted to be on the right side of it.

“I will never vote for @realDonaldTrump. Join me and add your name at NeverTrump.com,” wrote Patrick Ruffini, the founder of a Washington political media firm.