"She needs to go first, as always, Brett then needs to respond, and then it's time to take the vote", Fleischer said.
At issue are logistics - Christine Blasey Ford's security, her questioners, the placement of reporters and who is allowed in the hearing room.
But the White House would have to ask for it.
Asked if he would ask the FBI to open a deeper investigation, Trump said he was content to "let the senators do it". Grassley has instead scheduled a hearing for next Monday for both Ford and Kavanaugh to testify about the incident. A Republican aide didn't dispute the figure, but said those updates can be relatively minor, such as adding a nominee's tax records or educational information that had been inadvertently excluded. Almost 3 in 10 say they don't know if Kavanaugh should be confirmed. Trump and other Republicans, cautious of alienating women, have treated Ford carefully while calling for a quick vote.
The accusation has jarred the 53-year-old conservative jurist's prospects for winning confirmation, which until Professor Ford's emergence last week had seemed all but certain.
Sara Fagen, another longtime friend who worked with Kavanaugh in the White House, told a story about how Kavanaugh helped her the day of the September 11, 2001 attacks.
Senate Majority Leader Mitch McConnell (R-KY) told listeners at the annual Values Voter summit to "keep the faith" and "not get rattled" by "tactics" being used to keep Supreme Court nominee Brett Kavanaugh off the bench.
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Even if she did, it doesn't have the authority to give an assignment to an executive branch agency such as the Federal Bureau of Investigation.
Miranda later removed the post, explaining, cryptically, that the post "served its objective", and that she "was not ready" for the media attention the post garnered - even though NBC News and other outlets reported Miranda's claims as a major break in the Kavanaugh story. Mazie Hirono, D-Hawaii, said alongside Gillibrand on Thursday.
Hirono spoke at an event on Capitol Hill to highlight a letter of support that was said to have been signed by more than 1,000 alumni of Ford's high school in Maryland.
Can the Senate Judiciary Committee enlist the FBI to investigate the claims of sexual assault brought by an accuser against Judge Brett Kavanaugh, nominee to the Supreme Court?
Buttons worn in support of Ford harken back to similar pins worn in to show support for Anita Hill in 1991. "And the reason you should know that: look how angry the left is, huh?" So does Sen. Dianne Feinstein, the ranking Democrat on that committee. Kavanaugh has said that he is also willing to testify again in front of the committee.
Trump went on to suggest that he already considers Kavanaugh likely to surmount the row and be confirmed to the lifetime appointment. She has said she believes Ford.
Republicans relented in the face of calls to have Kavanaugh and his accuser testify in public.