Republicans declared that an FBI report had exonerated Brett Kavanaugh of sexual assault allegations.
But Democrats said the five-day inquiry was "incomplete" because it was limited by the White House.
The Senate will hold a procedural vote on the nominee on Friday.
The likelihood of Judge Kavanaugh winning a full Senate vote appeared to increase on Thursday after two Republicans whose backing will be essential gave a positive account of the FBI inquiry.
If confirmed to the lifetime position on America's highest court, the 53-year-old is expected to help conservatives dominate the nine-member panel, which has the final say on issues such as abortion, gun control and voting rules.
As the vote neared, the judge defended his neutrality in a Wall Street Journal editorial titled, "I am an independent, impartial judge".
Addressing his angry testimony to the Senate Judiciary Committee, where he branded the allegations against him an "orchestrated political hit", he wrote: "I know that my tone was sharp, and I said a few things I should not have said."
What happened at the protests?
Thousands of mainly female demonstrators marched through the nation's capital on Thursday, starting at the appeals court where Judge Kavanaugh currently presides.
They converged on Capitol Hill and held a rally outside the Supreme Court, chanting: "Kavanaugh has got to go!"
Police rounded the protesters up in a Senate office building after they sat down and refused to budge.
A total of 302 people were detained, with comedian Amy Schumer and model Emily Ratajkowski among them.
There was another protest in front of Trump Tower in New York City.
What was the reaction to the FBI report?
President Trump and his fellow Republicans declared the FBI report had cleared their nominee, as they sounded increasingly confident Judge Kavanaugh would win confirmation.
Senators said the FBI had spoken to five witnesses connected to accusations by Christine Blasey Ford, who alleges a drunken Brett Kavanaugh pinned her down, tried to remove her clothing and covered her mouth when she tried to scream at a house in 1982.
Federal agents are also said to have spoken to four other witnesses involving a separate accusation by Deborah Ramirez, who claims the nominee exposed himself to her when they were both were at Yale University. He denies both allegations.
"This investigation found no hint of misconduct," Senate Judiciary Committee chairman Chuck Grassley said in a statement.
Senate Republicans plan a procedural "cloture" vote at 10:30 on Friday (14:30 GMT), which is required to move to a final vote, scheduled on Saturday at around 17:30 (21:30 GMT).
But Democratic Senator Dianne Feinstein said the FBI report was "the product of an incomplete investigation", saying key corroborating witnesses had been snubbed. Another Democratic Senator, Richard Blumenthal, told reporters it was a "whitewash".
White House spokesman Raj Shah said: "What critics want is a never-ending fishing expedition into high school drinking."
One Republican Senator, John Cornyn, raised eyebrows by telling his party this was "our Atticus Finch moment", a reference to the lawyer in classic novel To Kill A Mockingbird who refutes a false rape allegation.
What did undecided senators say?
Given that Republicans have a razor-thin 51-49 margin of control in the Senate, the party can potentially only afford one defection if it wants to confirm Judge Kavanaugh to the Supreme Court, assuming Democrats vote the same way.
His nomination has been at the mercy of three wavering senators, but two of those - Jeff Flake and Susan Collins - appeared to respond positively to the FBI report.
Another wavering Republican senator, Lisa Murkowski of Alaska, reportedly met sexual assault survivors in her office on Thursday.
Complicating matters, the office of Republican Steve Daines said he was planning to attend his daughter's wedding in Montana on Saturday - meaning he would not be around to vote.
Another Republican, Cory Gardner, who previously said he would back Judge Kavanaugh, is yet to decide how he will vote, the Denver Post reported.
A previously undecided Democratic Senator, Heidi Heitkamp, said she would vote against Judge Kavanaugh, citing "concerns about his past conduct".
And Senator Joe Manchin of West Virginia, the only Democrat who remains undecided, said he would finish reading the FBI report on Friday morning.
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