Analysis by Stephen Collinson, CNN

(CNN) -- Democrats are demanding an immediate halt to Brett Kavanaugh's nomination process after his increasingly troubled hopes of reaching the Supreme Court were hit by a new allegation of sexual misconduct as a young man.

Kavanaugh quickly denied the new accusation by a female former fellow student about an alleged incident when he was at Yale University in the early 1980s. He branded the story reported by The New Yorker as part of a smear campaign by Democrats, a charge echoed by the White House.

The fresh trouble for Kavanaugh emerged hours after arrangements were finally locked in for a Senate hearing on Thursday at which his first accuser, Christine Blasey Ford, will allege that he sexually assaulted her when they were teenagers in high school.

The top Democrat on the Senate Judiciary Committee, Dianne Feinstein, responded to the new allegation by calling on the Republican committee chairman, Sen. Chuck Grassley, to order an "immediate postponement" of any further action on Kavanaugh's nomination.

Her intervention is likely to focus extra scrutiny on the accusation reported by The New Yorker and to raise the stakes even further for Thursday's hearing at which Kavanaugh is expected to present a vehement defense, which now looms as crucial for his confirmation hopes.

"I also ask that the newest allegations of sexual misconduct be referred to the FBI for investigation, and that you join our request for the White House to direct the FBI to investigate the allegations of Christine Blasey Ford as well as these new claims," Feinstein wrote.

Grassley's office issued a statement accusing Democrats of again actively withholding information from the rest of the committee only to drop it at "politically opportune moments."

"It increasingly appears that they are more interested in a political takedown than pursuing allegations through a bipartisan and professional investigative process," Grassley's spokesman Taylor Foy said, while pledging to evaluate the new allegations.

Kavanaugh was nominated by President Donald Trump to be the man who would enshrine a conservative majority on the Supreme Court for a generation.

But the allegations against him have emerged as a severe complication for Republicans, who are under intense pressure from their grass roots to swiftly confirm him while they seek to mitigate further damage with women voters who strongly favor Democrats in November's midterm elections.

If Kavanaugh is eventually confirmed, it will be by the tightest of margins because Republicans can only lose one vote in the Senate if all the Democrats stick together.

So Sunday's developments and Thursday's hearing will intensify pressure on two of the Republicans seen as the most likely to flip, Maine's Sen. Susan Collins and Alaska Sen. Lisa Murkowski. Outgoing Arizona Sen. Jeff Flake, who sits on the Judiciary Committee, is also a potential worry for the White House.

There was no immediate reaction to Sunday's new allegation from any of that trio.

A new allegation

The New Yorker story focuses on an allegation made by Deborah Ramirez, 53, who was at Yale with Kavanaugh and said she remembers him exposing himself to her at a dormitory party.

In a statement, Kavanaugh issued a strong denial.

"This alleged event from 35 years ago did not happen," he said in a statement. "The people who knew me then know that this did not happen, and have said so. This is a smear, plain and simple. I look forward to testifying on Thursday about the truth, and defending my good name -- and the reputation for character and integrity I have spent a lifetime building -- against these last-minute allegations."

Kerri Kupec, a White House spokeswoman also issued a statement.

"This 35-year-old, uncorroborated claim is the latest in a coordinated smear campaign by the Democrats designed to tear down a good man," the statement said. "This claim is denied by all who were said to be present and is wholly inconsistent with what many women and men who knew Judge Kavanaugh at the time in college say. The White House stands firmly behind Judge Kavanaugh."

Ramirez was initially hesitant to speak publicly, she told the magazine, partly because her memory contained gaps because she had been drinking at the time of the alleged incident. She was unsure of Kavanaugh's role in the incident at first, but after six days of carefully assessing memories and consulting with her attorney, Ramirez told The New Yorker she felt confident enough in her recollections to say she remembers it was Kavanaugh who had exposed himself.

A classmate of Ramirez's who was not at the party and who declined to be identified, told the magazine that he is "one hundred per cent sure" that either on the night of the party or in the next day or two he was told Kavanaugh was the student who exposed himself to Ramirez.

Several classmates of Ramirez interviewed by The New Yorker or who issued statements to the magazine said they had no memory of the alleged incident or disputed her account of events.

CNN has not independently confirmed The New Yorker's reporting.

Despite Kavanaugh's denials, the new allegation will add even more significance to Thursday's hearing, and may cause new pressure on Republicans to reverse their refusal to ask the FBI to reopen its background check on the nominee, who is currently an appeals court judge.

Kavanaugh is likely to face intensely embarrassing questions at the hearing from Democrats about his drinking, his sexual history and his behavior as a young man, both at Georgetown Prep, a private school outside Washington, and at Yale in the 1980s.

Kavanaugh has vehemently denied he assaulted Ford as a drunken teenager at a party. But he is now facing a fight for his reputation as he battles to keep a cherished prize, a lifetime appointment to the Supreme Court from slipping from his grasp before millions of TV viewers.

Though he has repeatedly asked for a chance to give his side of the story, the fact he has to testify must be seen as a weakening of Kavanaugh's position, since had Ford not agreed to appear, it is likely he would already be days away from being confirmed by the Senate.

And there is always the risk that however credible his presentation, political forces unleashed by the hearing evolve in unexpected ways, defy attempts by his supporters to control them and ultimately weaken and even destroy his nomination.

There is so far no indication that Republican leaders on Capitol Hill or in the White House might begin to consider whether the controversy over Kavanaugh's past is beginning to hurt his chances of confirmation. But any nomination that becomes becalmed is vulnerable to new attacks and information that could weaken the momentum towards confirmation.

CNN's Kaitlan Collins reported Sunday that multiple senior White House officials had privately expressed concerns last week that a second Kavanaugh accuser would emerge. At least three senior aides said last week they were confident Kavanaugh would be confirmed but warned a second accusation could derail his nomination altogether.

Ford agrees to testify despite complaints over process

After days of contentious deadline nudging negotiations, Ford's lawyers announced on Sunday that their client would take part in a hearing on Thursday, even though several disputes about the terms of the hearing remain unresolved.

"Despite actual threats to her safety and her life, Dr. Ford believes it is important for Senators to hear directly from her about the sexual assault committed against her," said a statement from her lawyers.

One of the biggest risks of Thursday's hearing is that it solves nothing.

It's possible, given accounts of her character by friends who have appeared on television, that Ford emerges as poised and courageous as she makes her allegation.

But there's also a chance Kavanaugh, who has been practicing for his testimony for days with White House lawyers, also makes a believable case as he testifies after Ford has made her allegation.

Democrats are furious that Grassley, of Iowa, will not call witnesses requested by Ford, and that Trump has refused to order the FBI to re-open the background check process to encompass the alleged assault back in the 1980s.

There are also signs that many Republicans have already made up their minds.

"What am I supposed to do? Go ahead and ruin this guy's life based on an accusation?" asked South Carolina Republican Sen. Lindsey Graham on "Fox News Sunday," arguing that Ford's case would not meet the standards of evidence required in a court of law.

Democrats, however, charged that Grassley's limits on the scope of the hearing reflect indifference to the suffering of a woman who said she was assaulted.

On Sunday, Hawaii Democratic Sen. Mazie Hirono told CNN's Jake Tapper that the credibility of Kavanaugh's denials should be called into question because of what she argued were his dishonest accounts of how he decides cases based on the merits and not on politics.

"His credibility is already very questionable in my mind and in the minds of a lot of my fellow Judiciary Committee members," Hirono said on "State of the Union."

"He has an ideological agenda, is very outcome-driven."