Washington (CNN) Brett Kavanaugh launched a bold effort to save his nomination to the US Supreme Court on Monday, lashing out at "smears" and a "grotesque and obvious character assassination" following the emergence of a new allegation of inappropriate sexual behavior.

Kavanaugh made clear that he was having no thoughts of folding his nomination, despite allegations dating to the 1980s, and warned that if his candidacy failed, it would deter people of all political persuasions from entering public service.

"There is now a frenzy to come up with something -- anything -- that will block this process and a vote on my confirmation from occurring," Kavanaugh wrote in a letter to the Senate Judiciary Committee leaders, and made clear he intends to defend himself at a hearing Thursday that will also feature testimony from his original accuser, Christine Blasey Ford.

"The coordinated effort to destroy my good name will not drive me out. The vile threats of violence against my family will not drive me out. The last-minute character assassination will not succeed," he wrote.

Kavanaugh's firm personal defense came as President Donald Trump and other top Republicans made a show of rallying round his nomination, sending a signal that the fresh allegations would not, for now, derail his hopes of serving on the court.

"(F)or people to come out of the woodwork from 36 years ago and 30 years ago and never mentioned it and all of a sudden it happens, in my opinion it's totally political," Trump said in New York. "It's totally political."

The President called his nominee "a fine man with an unblemished past."

He said later on Monday that it would be "sad" if Kavanaugh's nomination was upended by the allegations.

"His family has suffered," Trump said. "His family has suffered. What's going on is not something that should happen. Brett Kavanaugh is an absolute, outstanding person. Hopefully he will be confirmed quickly."

Kavanaugh was scheduled to appear with his wife for a sit down interview on Fox News Monday evening. In a clip aired before the full interview, Kavanaugh said he would not let the allegations kill his nominations.

"I'm not going to let false accusations drive us out of this process," Kavanaugh told Fox News. "We're looking for a fair process where I can be heard defending my integrity, my life-long record ... of promoting dignity and equality for women, starting with the women who knew me when I was 14 years old. I'm not going anywhere."

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. Ford had previously alleged that he sexually assaulted her at a house party in the Washington, DC, suburbs when they were teenagers in high school -- an accusation the judge strongly denies.

The top Democrat on the Senate Judiciary Committee, Dianne Feinstein, responded to the new allegation on Sunday night 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.

In a sign that the GOP is not willing to cut Kavanaugh lose, at least yet, South Carolina Sen. Lindsey Graham, who sits on the Judiciary Committee, accused Democrats of causing the "total collapse of the traditional confirmation process for a Supreme Court nominee."

"It is being replaced by a game of delay, deception, and wholesale character assassination," Graham said in a statement.

Kavanaugh was nominated by 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.