The fallout from the video and Mr. Trump’s more combustible attitude has already shown signs that it is turning off independent voters and women. Christian conservatives, an important segment of the Republican base, have also expressed concern that Mr. Trump has taken his scorched earth approach too far.

“This past week, the latest (though surely not last) revelations from Trump’s past have caused many evangelical leaders to reconsider,” Andy Crouch, the executive editor of the evangelical publication Christianity Today, wrote in an editorial published Monday. “The revelations of the past week of his vile and crude boasting about sexual conquest — indeed, sexual assault — might have been shocking, but they should have surprised no one.”

The essay went on to argue that many Christians have been supporting Mr. Trump for strategic reasons, largely based on the notion that he was on their side when it came to social issues and the direction of the Supreme Court, but that ultimately social conservatives could not be blind to Mr. Trump’s behavior.

“Enthusiasm for a candidate like Trump gives our neighbors ample reason to doubt that we believe Jesus is Lord,” Mr. Crouch wrote. “They see that some of us are so self-interested, and so self-protective, that we will ally ourselves with someone who violates all that is sacred to us — in hope, almost certainly a vain hope given his mendacity and record of betrayal, that his rule will save us.”

However, not everyone is turning against Mr. Trump, with four weeks to go until Election Day. In a speech at Liberty University in Virginia on Monday, Ralph Reed, a prominent evangelical leader, made a forceful case for why Mr. Trump remained a better choice than Mrs. Clinton despite the offensive video that was revealed last week.

And Senator Marco Rubio of Florida, who fought bitterly with Mr. Trump during the Republican primary campaign, said on Tuesday that he was not ready to abandon Mr. Trump.

For his part, Mr. Trump suggested on Tuesday that he now felt emboldened by his campaign’s new leadership team and the fact that he was no longer trying to please establishment Republicans by restraining himself.