Some Republican senators said at least a portion of the document should be available for public review.
Those GOP senators, along with Democrats Heidi Heitkamp of North Dakota and Joe Manchin of West Virginia, have yet to declare how they will vote on Kavanaugh.
Senate majority leader Mitch McConnell is "hell-bent on getting this done" this week, one Democrat said.
"[McConnell] said we would vote this week", Senate Majority Whip John Cornyn (R-TX) told reporters, Fox News reported.
If they don't have the votes, the nomination fails.
He and Dr. Christine Blasey Ford, who has accused Kavanaugh of sexually assaulting her when they were both teenagers, testified before the Senate Judiciary Committee last week. If Kavanaugh clears Friday's procedural hurdle, that would set up a final confirmation vote as early as Saturday.
Officials were expected to be sending the Federal Bureau of Investigation report to the Senate Judiciary Committee later Wednesday. She would not say if they would affect her vote. I don't know. I don't know. "I don't know. Upstairs". I don't know - but I had one beer. 'I don't remember.' Where is the place?
He went on to say: "A man's life is in tatters". Jeff Flake (R-AZ), who forced the committee's hand over the investigation, spoke with Today on Wednesday morning where he called the remarks "kind of appalling".
Speaking briefly to reporters, Collins said: "The president's comments were just plain wrong".
The letter claims the Republican staffers have selectively disclosed evidence and worked to "undermine the credibility of the women who have come forward". "The President's comments yesterday mocking Dr Ford were wholly inappropriate and, in my view, unacceptable". He had previously called Ford a "very credible witness", while continuing to back Kavanaugh.
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He also lamented the cost of Ford's allegations to Kavanaugh and insinuated that she was part of a conspiracy by the Democrats to discredit him.
President Donald Trump's mockery of Christine Blasey Ford sparked an immediate backlash Wednesday among two critical Republican swing votes on the nomination of Supreme Court hopeful Brett Kavanaugh, with Sens.
He said the pressure will be on Democrats in predominantly red states that Trump won in 2016, such as Sens.
That means if all the Democrats vote against Mr Kavanaugh, Mr Trump could not afford to have more than one Republican oppose his nominee, with Vice President Mike Pence casting a tie-breaking vote.
Senator Joni Ernst from Iowa, said Ford's story hasn't been corroborated and people should be presumed innocent until proved guilty.
Opposition among Americans to Kavanaugh has increased since last week's hearing, Reuters/Ipsos polling data showed on Wednesday.
Administrators at the prestigious college emailed students late Monday to say Kavanaugh "indicated that he can no longer commit to teaching his course in January Term 2019, so the course will not be offered".
But Hamilton predicts the Democrats' effort to block Kavanaugh ultimately will fail - and the judge will be confirmed to the Supreme Court.
Amid McConnell's remarks Wednesday night, Trump tweeted that there was "such enthusiasm and energy for Judge Brett Kavanaugh". It's just not right.
At a White House briefing, Trump's spokeswoman Sarah Sanders defended his remarks in MS and said he was not concerned the comments may have jeopardized the votes of key senators.