Republican leaders began to abandon Donald J. Trump by the dozens on Saturday after the release of a video showing him speaking of women in vulgar sexual terms, delivering a punishing blow to his campaign and plunging the party into crisis a month before the election.
Fearing that his candidacy was on the verge of undermining the entire Republican ticket next month, a group of senators and House members withdrew support for him, with some demanding that he step aside. Mr. Trump, however, vowed to stay in the race.
The list of party figures publicly rejecting Mr. Trump included a host of prominent elected officials, perhaps most notably Senator John McCain of Arizona, the 2008 nominee.
“I thought it important I respect the fact that Donald Trump won a majority of the delegates by the rules our party set,” Mr. McCain said in a statement. “But Donald Trump’s behavior this week, concluding with the disclosure of his demeaning comments about women and his boasts about sexual assaults, make it impossible to continue to offer even conditional support for his candidacy.”
And in an unheard-of rebuke by a running mate, Gov. Mike Pence of Indiana, the Republican vice-presidential candidate, declined to appear on Mr. Trump’s behalf at a party gathering in Wisconsin and offered him something of an ultimatum on Saturday afternoon.
Mr. Pence said in a statement that he was “offended by the words and actions described by Donald Trump” in the video, and cast Mr. Trump’s second debate with Hillary Clinton, on Sunday, as an urgent moment to turn around the campaign.
“I do not condone his remarks and cannot defend them,” Mr. Pence said, adding, “We pray for his family and look forward to the opportunity he has to show what is in his heart when he goes before the nation tomorrow night.”
By Saturday evening, no fewer than 36 Republican members of Congress and governors who had not previously ruled out supporting Mr. Trump disavowed his candidacy, an unprecedented desertion by the institutional Republican Party of its own standard-bearer just a month before Election Day.
The growing wall of opposition recalled the determination of the party establishment this year to deny Mr. Trump the nomination in the first place. He easily swatted away that effort, but Mr. Trump now finds himself in a far more precarious state. Facing a more vast and diverse electorate, his lightly organized campaign was already listing before the videotape was released.