Analysis by Stephen Collinson, CNN

(CNN) -- Brett Kavanaugh's accuser now has a name, and the Republican Party's bid to swiftly lift him onto the Supreme Court may be spinning out of control.

The coming hours could decide whether the GOP can stabilize the confirmation process of President Donald Trump's nominee or whether his hopes of being the man to enshrine a conservative majority for a generation could begin to crumble.

California professor Christine Blasey Ford's emergence sent a jolt through the White House and Capitol Hill on Sunday, prompting demands from Democrats for all votes on Kavanaugh to be put on hold pending an investigation. Even some Republicans conceded the issue needed to be addressed before things go further.

Ford told The Washington Post that she went public because of the magnitude of Kavanaugh's appointment.

"Now I feel like my civic responsibility is outweighing my anguish and terror about retaliation," Ford told the paper, ahead of what is likely to be an ordeal characterized by political attacks and fearsome scrutiny of her life, family, mental health and political leanings.

Ford's gambit looked set to provoke the kind of spectacle triggered by attorney Anita Hill's harassment claims against Clarence Thomas during his confirmation process in 1991. If so, it will elevate the debate on Kavanaugh from a Washington squabble to a national zeitgeist moment.

The showdown will unfold amid the still-unsettled politics of the #MeToo movement, which has transformed the way allegations by women of sexual harassment by now-powerful men, even from decades ago, are viewed by society. But it also takes place at a pivotal moment for the conservative movement, which is within reach of a goal it has pursued for decades of cementing a majority on the Supreme Court at a time of key rulings on issues like abortion, same-sex marriage and the role of religion in American life.

That turbulent backdrop has not, so far, changed the relentless math of the GOP's Senate majority, but it could significantly increase the political cost to the party of confirming him.

Ford's move puts a human face on what had previously been more an indirect, impersonal controversy and made it more difficult for Republicans simply to dismiss what, after all, is an accusation of a crime against a pivotal nominee.

Democrats on Sunday demanded that a Senate Judiciary Committee vote to move forward on Kavanaugh's confirmation, due on Thursday, should be put on hold to allow time for a full investigation, grabbing a fresh opening to try to slow his progress after one of the nastiest confirmation fights in recent years.

Until Sunday, there was a feeling among many Republicans that Kavanaugh had been unfairly targeted, and was the victim of an 11th-hour Democratic bid to destroy his nomination. California Sen. Dianne Feinstein had known about the allegations for weeks, but did not bring them up during the confirmation hearings. That feeling was especially acute because Ford had chosen to make her allegations anonymously -- although advocates pointed out that the privacy of women who say they have been assaulted must be preserved.

Kavanaugh has categorically and unequivocally denied he did anything wrong, despite Ford's claims that at a party in the 1980s, he was drunk, forced himself upon her and tried to take off her clothes.

Furthermore, Ford did not appear to report the alleged assault at a house in Washington's Maryland suburbs at the time. Kavanaugh was never investigated over it and the alleged assault was not uncovered by multiple FBI background checks conducted during his career in politics and as a judge.

Ford says she has lived with the aftereffects of the alleged assault for years and that it caused her trauma and symptoms of post-traumatic stress disorder. Her account in the Post offers far more detail than has previously been available, another factor that could influence the politics of the nomination this week.

Kavanaugh, meanwhile, is seeing his entire career and reputation put on the line in a controversy that is certain to draw in his young family and will surely tarnish his image even if he is cleared of wrongdoing and is confirmed to sit on the Supreme Court.

The choice for Republicans

The sudden developments place Republican senators who the White House is relying on to shepherd his nomination with a choice.

Will they stick together in the view that Kavanaugh is being unfairly treated on accusations that date from decades ago? Or will they be forced by political and public pressure to agree to an investigation that could slow his confirmation?

Presidential nominations often unfold according to an intangible logic. Even candidates that look unassailable can be suddenly weakened by sudden disclosures. Once a nominee is wounded, his or her confirmation hopes can quickly splinter as political support fractures, so Kavanaugh can ill afford any roadblocks, even if his prospects look good now.

And any slowed momentum could give time for more problems to emerge and allow his fate to become even more embroiled in the midterm elections, which are only seven weeks away.

Pressure will be especially intense on Maine Sen. Susan Collins and Alaska Sen. Lisa Murkowski, who have been seen as two Republicans who could be wavering on Kavanaugh over the issue of abortion.

If those two senators oppose Kavanaugh and all of the Democrats stick together, his nomination could be defeated.

So far, Collins is not saying whether the allegations, which first emerged in a letter sent in July that reached Democratic Sen. Dianne Feinstein, would sway her vote on the nomination.

"I don't know enough to create the judgment at this point," she told CNN on Sunday evening.

Ford's emergence might also change the political equation for Democrats running for re-election in red states, offering them an excuse to stick with their party despite calls of conservative constituents to support Kavanaugh.

Republican Senate Judiciary Committee chairman Chuck Grassley said that it was "disturbing" that such "uncorroborated" allegations had emerged ahead of the committee vote. But there was just a hint of an opening for Democrats.

A spokesman said that the Iowa senator was working to set up calls with Kavanaugh and Ford before Thursday's vote, and South Carolina Republican Sen. Lindsey Graham raised the possibility that the committee should hear testimony from Ford.

When asked about delaying the vote, Murkowski told CNN the committee should consider doing so.

"I think that might be something they might have to consider, at least having that discussion," she said. "This is not something that came up during the hearings. And if there is real substance to this, it demands a response."

And in another sign of potential trouble for Kavanaugh, two senators who are not running for re-election and are therefore insulated somewhat from the Republican base, Arizona's Jeff Flake and Tennessee's Bob Corker, said they need to hear more from Ford.

"I've made it clear that I'm not comfortable moving ahead with the vote on Thursday if we have not heard her side of the story or explored this further," the Arizona senator told the Post.

The Supreme Court's #MeToo moment

The future trajectory of Kavanaugh's nomination is especially difficult to predict because of the change in how alleged sexual assaults are now handled in public life, following a long series of scandals that have felled key figures in politics, the media and Hollywood in recent months.

Democratic Senate Minority Leader Chuck Schumer played directly into the idea that the #MeToo campaign had changed everything.

"For too long, when woman have made serious allegations of abuse, they have been ignored. That cannot happen in this case," Schumer said.

At the very least, the decision of Ford to unmask herself offered Democrats a rallying point as they seek to make the Kavanaugh nomination and the fate of the Supreme Court generally a key issue in the midterm elections.

Democratic senators had previously assailed Kavanaugh in his hearing over abortion and past rulings on corporations. They had also condemned the White House for withholding tens of thousands of documents relevant to Kavanaugh's time as a key aide to President George W. Bush.

But Ford's emergence now gives Democratic candidates, especially those in suburban House districts where women voters are crucial, a chance to make some GOP lawmakers pay a significant price for the party's support of Kavanaugh.

The spectacle of white, middle-aged or elderly men on the GOP bench voting to confirm Kavanaugh in the committee could prove a damaging image in districts that could turn on a younger, more diverse electorate.

Yet there are also good reasons -- aside from a feeling that Kavanaugh is being treated unfairly -- for Republicans to stick by Trump's pick.

Kavanaugh would enshrine the right's majority on the court, possibly for generations and make Chief Justice John Roberts, a conservative, the swing vote on key issues.

So while some Republican senators could get squeamish over the allegations against Kavanaugh, they are under fierce pressure from their voters to do nothing to deny Trump another win and the conservative movement an existential triumph.