WASHINGTON (CN) – Brett Kavanaugh vows in a new letter to the Senate Judiciary Committee that he will “not be intimidated” into withdrawing from consideration as Donald Trump’s nominee to the U.S. Supreme Court, saying the “smears” against him “debase the public discourse” and are “a threat to any man or woman who wishes to serve our country.”

Kavanaugh’s letter was a response to Senate Democrats who called over the weekend for an end to his nomination to the Supreme Court after a second woman came forward accusing him of sexual misconduct.

But Kavanaugh is pushing back, contending “there is now a frenzy to come up with something —anything — that will block this process and a vote on my confirmation from occurring.”

The New Yorker on Sunday published the account of Deborah Ramirez, who says Kavanaugh put his penis in her face at a drunken party in a dorm during Kavanaugh’s freshman year at Yale. Ramirez is the second woman to accuse Kavanaugh of sexual misconduct, with Palo Alto University professor Christine Blasey Ford having already accused the nominee of forcing her into a bedroom, pinning her down and trying to remove her clothes at a high school party in the 1980s.

Kavanaugh has denied both allegations, saying in a statement Sunday night he looks forward to defending against the claims at a Senate Judiciary Committee hearing scheduled for this week.

“This alleged event from 35 years ago did not happen,” Kavanaugh said in a statement, referring to Ramirez’s allegation. “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.”

On Monday, President Donald Trump weighed in, saying sexual assault allegations against Supreme Court nominee Brett Kavanaugh are “totally political.”

“For people to come out of the woodwork from 36 years ago and 30 years ago and — never mentioned it, all of a sudden it happens — in my opinion, it’s totally political. It’s totally political,” Trump said. “There’s a chance that this could be one of the single most unfair, unjust things to happen to a candidate for anything.”

The New Yorker article notes the magazine was not able to confirm with other people that Kavanaugh was at the party. One former classmate of Ramirez’s backed up her claims, saying someone told him about the incident either the same night or within a few days of the party. Others who attended Yale with Kavanaugh and Ramirez disputed the claims, calling the alleged incident out of character for Kavanaugh.

The same is true for Ford’s allegation, as several people whom Ford had identified as being at the party have either denied or said they did not remember such an incident.

The allegations that have surfaced against Kavanaugh in the last week and a half have cast a cloud over what once seemed to be an inevitable confirmation.

The Judiciary Committee has scheduled a hearing on Thursday to hear from both Ford and Kavanaugh, a product of lengthy negotiations between Senator Chuck Grassley, the Iowa Republican who chairs the committee, and Ford’s attorneys last week.

But Senator Dianne Feinstein, the top Democrat on the Judiciary Committee, called on Grassley to pause Kavanaugh’s nomination in light of Ramirez’s allegations, repeating her desire that the FBI look into both women’s claims.

“We need a fair, independent process that will gather all the facts, interview all the relevant witnesses and ensure the committee receives a full and impartial report,” Feinstein wrote to Grassley Sunday. “Should the White House continue to refuse to direct the FBI to do its job, the committee must subpoena all relevant witnesses.”

Senator Kirsten Gillibrand, D-N.Y., called for Kavanaugh’s withdrawal on Twitter shortly after the New Yorker piece published.

“Enough is enough,” Gillibrand wrote. “One credible sexual assault claim should have been too many to get a lifetime appointment to the Supreme Court and make decisions that will affect millions of women’s lives for generations. Two is an embarrassment. It’s time for a new nominee.”

Grassley’s office said aides for the senator learned about Ramirez’s allegations when the New Yorker published its story. The report says “senior Republican staffers” learned about them last week, though it did not say whose office the staffers worked in.