Prof Ford and the Senate Judiciary Committee are engaged in a stand-off, and time is running out, the BBC's Gary O'Donoghue reports from Washington.
They said Ford's "strong preference" is that "a full investigation" be completed before her testimony, but stopped short of demanding an FBI probe and seemed to suggest that she would testify without one. "Chrissy is not someone who chooses to be in the spotlight".
Christine Blasey Ford came out publicly as the woman who made the allegations in a September 16 story in The Washington Post.
The Monday hearing already represents a delay to Kavanaugh's confirmation process.More news: Nokia 5.1 Plus launching in India on September 24th as Flipkart
It is plausible that Judge Kavanaugh and Ms. Blasey Ford would know each other.
In an email to committee aides, the lawyer for Christine Blasey Ford says that it is "not possible" for her client to appear on Monday, adding that the committee's selection of that day is "arbitrary in any event".
"We started out - I didn't like him, he didn't like me", Trump said.
Ford has said through her lawyer that won't do.
A new Wall Street Journal/NBC News poll found that Kavanaugh's nomination faces growing opposition from voters, with 38 percent in opposition, compared to 29 percent in the same poll last month.
Republicans have rejected her request to bring in the FBI, saying the Judiciary Committee can do its own investigation. "Dear Professor Ford, we know how hard it is to stand up to powerful people", they say. They chanted, "We believe Anita Hill. Do the right thing, for a change", Hirono said Tuesday, stealing the show at a press conference that featured several high-profile Democrats.More news: Undercover Investigation Reveals Ticketmaster Hires Professional Scalpers to Drive Ticket Prices
Republicans also fear that if the nomination is delayed any further, that remaking of the Supreme Court could be endangered by a possible Democratic sweep in the congressional midterm elections set to take place in seven weeks. She's been listening to that interview, and she's going to talk with us more about this controversy over Brett Kavanaugh.
Ford alleges that more than 30 years ago, when she and Kavanaugh were teenagers in high school, he sexually assaulted her at a party - holding her down, groping her, attempting to remove her clothes and putting his hand over her mouth when she tried to shout. "Fairness and respect for her situation dictate that she should have time to deal with this".
"Senate Republicans are attempting to make Dr. Blasey Ford testify on just a few days' notice - without having the Federal Bureau of Investigation follow up on her allegations and provide a report first", said the letter, which was spearheaded by Sens.
It remains unclear whether Ford will attend or if the hearing will occur without her.More news: True Detective director to make next Bond movie