(CNN) The Republican Party is in a meltdown unlike anything it has experienced in modern times -- and it's unfolding just one month before Election Day.

Many in the GOP are reeling from shock, revulsion and utter confusion about what to do next after a video surfaced Friday of Donald Trump talking about women in crude and aggressive sexual terms.

The topics discussed included his daughter Ivanka's physique, having sex with women during their menstrual cycles, threesomes, and checking out of relationships with women after they turn 35.

The fallout on Saturday revealed a party in chaos as dozens of Republicans either pulled their support for Trump or said his running mate, Mike Pence, should lead the ticket. Pence, the governor of Indiana, criticized Trump and canceled a scheduled appearance in Wisconsin on behalf of the campaign later Saturday.

Even Trump's wife, Melania, who has kept a low profile in recent months, released a statement saying Trump's comments were "offensive."

"This does not represent the man that I know," she said. "He has the heart and mind of a leader. I hope people will accept his apology, as I have, and focus on the important issues facing our nation and the world."

Huddle at Trump Tower

Trump's closest advisers, including New Jersey Gov. Chris Christie and former New York Mayor Rudy Giuliani, gathered at Trump Tower to plot a path forward. But in a sign of the extraordinary resistance to Trump that has developed over the past 24 hours, many in the party consulted the rules of the Republican National Committee to decide whether there's any possibility of dropping the billionaire from the ticket -- an option that seems easier said than done.

For now, the RNC has put a temporary pause on its mail operations that are part of the committee's victory operation to assess the current situation and decide if they need to change their message on mailings and other get-out-the-vote operations, according to a top RNC official.

Through it all, Trump seems determined not to be fazed by the crisis enveloping his campaign.

"I'd never withdraw. I've never withdrawn in my life," Trump told The Washington Post . "No, I'm not quitting. I have tremendous support."

He told The Wall Street Journal there is "zero chance I'll quit."

The GOP nominee enjoys a strong base of support among disaffected Republican voters, and there are no immediate signs that his most loyal backers will split with a man they view as their champion in confronting a hated political establishment. In fact, the revolt of the establishment wing of the party against the GOP nominee could further embolden Trump's supporters.

Trump briefly emerged from Trump Tower Saturday afternoon to greet his supporters, who cheered "USA! USA!"

Mess enveloping campaign

The mess enveloping the Trump campaign is just the latest stunning lurch of a wild presidential race that has repeatedly tested the limits of convention, credulity and even decent political discourse owing to the presence of Trump. Most immediately, the crisis elevates the GOP nominee's crucial second debate clash Sunday night with Hillary Clinton at Washington University in St. Louis into an extraordinarily important moment for Trump's White House campaign.

Even before then, the fragile marriage of convenience between the GOP and Trump was splintering.

Pence abruptly canceled plans to appear with House Speaker Paul Ryan in Wisconsin. Pence has repeatedly defended Trump despite his long history of controversial statements and positions. His decision not to show up sent a signal that he didn't want to personally represent Trump at an important Republican Party event.

Pence issued a statement saying he was offended by the words and actions of his ticket mate.

"I do not condone his remarks and cannot defend them," Pence said. "I am grateful that he has expressed remorse and apologized to the American people. 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."

Pence's comments were an example of how Republican politicians are maneuvering amid the fast-changing political environment to protect their own futures as well as the short-term run-up to the election.

For her part, Hillary Clinton has largely stood by as the drama with Trump and the GOP unfolds. But the furor presents Clinton with a new challenge -- and opportunities -- as she prepares for Sunday's debate.

The former secretary of state must calibrate how she responds to the storm raging around Trump, and also prepare for the possibility that he will try to deflect it by bringing up the past infidelities of her husband, former President Bill Clinton.

Hillary Clinton was hunkered down and preparing for Sunday's debate with her top aides at the Doral Arrowwood, a Rye Brook, New York, hotel and spa, when The Washington Post published the bombshell video of Trump casually talking about sexual assault on Friday.

The tape changed Clinton's debate prep as the small group of advisers with her focused on how to prepare her on how she will respond. Based on those efforts, Clinton's top aides decided Saturday that the Democratic nominee will not respond to Trump's suggestive comments before tomorrow's debate and instead address them "early" in the debate, possibly in her opening statement.

Clinton's senior advisers made the decision after watching dozens of Republicans rescind their endorsements and feel there is no rush to get something out Saturday. The campaign thinks it is beneficial for them if her first response comes during what is expected to be a debate that draws more than 80 million people, maximizing the number of people who see her reaction.

Cutting Trump loose

Republicans steadily began cutting Trump loose Saturday.

New Hampshire Sen. Kelly Ayotte, locked in a tight re-election race, helped trigger an avalanche of top GOP figures away from Trump. Nevada GOP Senate candidate Joe Heck, competing in another competitive race, said he could no longer support Trump, though would not vote for Clinton.

Arizona Sen. John McCain also withdrew his support for Trump. In addition to the vulgar comments that surfaced Friday, McCain also cited Trump's controversial remarks earlier in the week about the "Central Park 5" -- saying he believed they were still guilty in a 1989 rape despite being exonerated years ago -- in making his decision.

"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. Cindy, with her strong background in human rights and respect for women fully agrees with me in this," McCain said.

"Cindy and I will not vote for Donald Trump," he continued. "I have never voted for a Democratic presidential candidate and we will not vote for Hillary Clinton. We will write in the name of some good conservative Republican who is qualified to be president."

Meanwhile, Ted Cruz, who only recently endorsed Trump after a brutal primary battle, is considering rescinding that backing, according to a source close to the Texas senator.

A handful of top operatives involved in GOP Senate races said the guidance from the Republican leadership in Washington is to do whatever it takes to insulate those campaigns from the Trump fallout.

"This comes from the top and it couldn't be more clear: Repudiate him, repudiate the remarks, and if you need to go beyond that, then don't hesitate and don't worry," said one Republican strategist working a difficult race for a GOP Senate incumbent.

"The presidential race is over," said a second GOP strategist working a key Senate race.

Three GOP sources familiar with conversations at the highest level of the party leadership said House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell would prefer Trump step aside, even though they understand the mess and confusion that would cause because early voting is under way, state ballots are mostly printed and deadlines for getting off the ballot have passed in most states.

Both Ryan and McConnell have condemned his remarks but neither has publicly called for him to quit the ticket. Sen. John Thune of South Dakota, a McConnell leadership deputy, did say Trump should step aside, and the GOP sources pointed to that as evidence of leadership thinking.

These sources said both congressional leaders are increasingly frustrated with RNC Chairman Reince Priebus, who has repeatedly promised them Trump would come to understand his role as nominee and his impact on other Republicans. And they said it had been relayed to Priebus that they expected the national organization to place protecting the congressional majorities first as questions about resources are decided in the final 30 days of the race.

Forcing Trump off the ticket

Republican sources say one option under consideration is ending the Joint Fundraising Agreement between the RNC and the Trump campaign so the RNC could focus its fundraising exclusively on critical down ballot races and encourage donors who were opposed to Trump to continue to support the party.

But the chance that the GOP could force Trump off its presidential ticket just a month before Election Day appears to be a long shot, not least because the election is already underway in some states in absentee and early voting.

In theory, there is a mechanism to replace Trump on the ticket should he rescind his pledge to stay in the race and drop out. The party rules allow RNC members to pick a new nominee in a state-by-state vote.

But any move to replace Trump would soon run into a legal minefield. There is no system in place, for instance, for states to recall votes or offer new ballots to Americans who have already voted in the election. Ballot access deadlines have already passed in some states so there would certainly be legal challenges.

One RNC member told CNN's Tom LoBianco that dumping Trump would be almost impossible.

"I don't think it's an option. Seriously. Ballots are printed. People are already voting. We just have to live with it."

Another RNC member said getting changes to balloting rules in 50 states was likely not going to work. "We are stuck and so is Pence," the person said.