Christine Blasey Ford, the first woman to come forward and accuse Kavanaugh of sexual misconduct, will testify along with Kavanaugh in a public hearing Thursday.
Ford's allegation and another accusation by a second woman have imperiled Kavanaugh's chances of confirmation to the lifetime appointment to the nation's highest court.
"I have no way of knowing", Feinstein told Fox News.
"Pray for Brett Kavanaugh and his family!"
On Mr Kavanaugh, Mr Trump stressed: "I am with him all the way".
"I look forward eagerly to hearing from both Dr. Ford and Judge Kavanaugh under oath this Thursday morning", he said.
A vote in the full Senate could happen as early as next Tuesday, senior Senate Republicans have said.
The Kavanaugh confirmation fight comes just weeks before November 6 congressional elections in which Democrats are trying to take control of Congress from Trump's fellow Republicans, against a backdrop of the #MeToo movement fighting sexual harassment and assault.
Republican Majority Leader Mitch McConnell of Kentucky accused Democrats of rushing to convict Kavanaugh and "destroy his good name" with unproven allegations, abandoning any presumption of innocence - a bedrock principle of American jurisprudence.
According to the affidavits, Ford revealed the assault in varying levels of detail between 2002 and Koegler's email in June.
Other institutions take serious action when confronted with sexual violence, but the Senate seems to engage in "an effort to lean in to bias", she said.
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Ms Ramirez described the alleged incident after being contacted by The New Yorker magazine. He says she named the attacker as Kavanaugh.
Interested in Supreme Court? The two met at a Mountain View, California, restaurant, where Ford arrived "visibly upset".
Ramirez's lawyer, John Clune, said in television interviews on NBC and CBS on Wednesday that she has not been invited to speak to senators. "She said that she had been nearly raped by someone who was now a federal judge".
"She told me that when she was a young teen, she had been sexually assaulted by an older teen", White says. A hearing is scheduled for Thursday.
Furthermore, Grassley said he was "unclear" why the claims by Ramirez had any bearing on Ford's testimony.
Rachel Mitchell, a sex crimes prosecutor from Arizona, will conduct the questioning, the Wall Street Journal reported.
Judge Kavanaugh has denied the allegations.
Kavanaugh categorically denies the allegations leveled by Ford and Deborah Ramirez, who accused him of sexual misconduct at a college party also more than three decades ago.
After the interview aired, the sense in the West Wing was relief that Kavanaugh was able to present an image to counter the allegations. Yet he appeared shaky at times. Trump dismissed her as part of a Democratic-led "con job" to keep Kavanaugh off the bench.
The affidavits are not the first challenges to Kavanaugh's denials.
Kavanaugh, a judicial conservative and Trump's second Supreme Court pick, was nominated to fill the vacancy created by Justice Anthony Kennedy's retirement. "The second accuser doesn't even know- thinks maybe it was him, maybe not". She said she clearly remembered that it was Kavanaugh, but she also acknowledged that she was extremely drunk and that she has significant gaps in her memory of the evening.