Senate majority leader Mitch McConnell is "hell-bent on getting this done" this week, one Democrat said.
He pledged that the full U.S. senate would begin voting on Mr Kavanaugh's nomination this week.
"It's time to put this sickening display behind us", McConnell said in remarks on the Senate floor earlier in the day. "The Senate will vote on this nomination this week".
"While we are limited in what we can say about this background investigation in a public setting, we are compelled to state for the record that there is information [in the tweet] that is not accurate", the Democrats wrote in their letter, without providing details.
"The White House confirmation that it will not allow the FBI to interview Dr. Blasey Ford, Judge Kavanaugh or witnesses identified by Deborah Ramirez raises serious concerns that this is not a credible investigation", she said in a statement.
"As Rachel Mitchell said in her memorandum to members on the Senate Judiciary Committee, the allegations of Christine Ford do not even rise to the level of preponderance of evidence, which is one of the lowest standards in legal work that exists", he explains. "Downstairs? Where was it - I don't know." - though Ford has consistently said that it was an upstairs bedroom. "I know this because I heard Brett and his friends using these terms on multiple occasions". "I don't know but I had one beer that's the only thing I remember!"
A man identifying himself as Ford's former boyfriend said in the letter he saw Ford coach a friend on how to be less nervous during a polygraph examination.
"There's no time and no place for remarks like that", Flake said in an interview with NBC News early Wednesday.
"I thought it was obviously insensitive and appalling, frankly".
Later Wednesday morning, Collins similarly told reporters that "the president's comments were just plain wrong". "Wholly inappropriate and entirely unacceptable" chimed in Murkowski.More news: Google will let you stream Assassin's Creed Odyssey from Chrome
Trump drew laughs from supporters at a rally Tuesday night with his rendition of how Ford answered questions at last week's hearing.
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.
Flake was instrumental last Friday in getting Trump to order an FBI investigation into the allegations against Kavanaugh, nominated by Trump for a lifetime job on the top USA court.
Trump limited the investigation to no more than a week.
Senators and aides have said that the file will contain forms of interviews conducted by the FBI - but not a conclusion from the bureau about who's telling the truth in the case.
Trump's fellow Republicans control the Senate by a 51-49 margin.
Trump later told the crowed that Kavanaugh was a deserving nominee.
Opposition among Americans to Kavanaugh has increased since last week's hearing, Reuters/Ipsos polling data showed on Wednesday. President Trump said, role-playing a conversation between a son and mother. This background check, requested by a trio of senators who are undecided on Kavanaugh's confirmation, will be different.
In a Twitter post on Wednesday, Trump did not back away from his rally comments, instead attacking Kavanaugh's Democratic critics.
Mr Trump said when he goes to political rallies, which are organised by Republicans, he sees that voters are angry at the "vicious and despicable" way Democrats are treating his nominee.