Brett M. Kavanaugh’s temperament and truthfulness came under increased scrutiny from lawmakers Tuesday, and President Trump mocked one of the women accusing the judge of sexual assault decades ago as the Senate pressed toward voting by week’s end on the Supreme Court nominee.

With Kavanaugh’s chance for a lifetime appointment to the high court at stake, Sen. Jeff Flake (R-Ariz.) — the Judiciary Committee member who had pushed to delay the vote so the FBI could investigate the allegations — criticized the tenor of the nominee at the hearing last week where Kavanaugh aggressively defended his innocence and sparred with Democratic senators.

Later Tuesday, at a rally in Southaven, Miss., Trump ridiculed Christine Blasey Ford, who accused Kavanaugh of sexually assaulting her at a small gathering at a house in the Washington suburbs more than 30 years ago. The FBI has also interviewed a second woman who accused Kavanaugh of sexual misconduct.

Specifically mentioning Ford’s inability to answer certain questions during her Senate testimony, Trump drew cheers and laughter from his supporters at the rally: “ ‘How did you get home?’ ‘I don’t remember.’ ‘How did you get there?’ ‘I don’t remember. ‘Where is the place?’ ‘I don’t remember.’ ‘How many years ago was it?’ ‘I don’t know.’ ”

He continued: “ ‘Upstairs? Downstairs? Where was it?’ ‘I don’t know. But I had one beer. That’s the only thing I remember.’ And a man’s life is in tatters.”

In a tweet after the rally, Michael Bromwich, an attorney for Ford, called Trump’s remarks “a vicious, vile and soulless attack” on his client.

Earlier in the day, Flake said at the Atlantic Festival he was “very troubled by the tone” of Kavanaugh’s testimony. “The interaction with the members was sharp and partisan, and that concerns me. And I tell myself, you give a little leeway because of what he’s been through, but on the other hand we can’t have this on the court. We simply can’t.”

Senate Republicans gave in to Democrats' demands to reopen the FBI investigation into Brett M. Kavanaugh, but the two sides are still pitted against each other. (Jenny Starrs/The Washington Post)

Flake’s comments came as Majority Leader Mitch McConnell (R-Ky.) promised that the Senate would vote on the nomination this week without any further delay. “We’ll have the opportunity to vote ‘no’ on the politics of personal destruction. We’ll have the opportunity to vote ‘yes’ on this fine nominee,” he said.

It was uncertain, though, whether McConnell would have the votes to confirm President Trump’s nominee. Flake and two other key Republicans — moderate Sens. Susan Collins (Maine) and Lisa Murkowski (Alaska) — are declining to say how they’ll vote until they see the results of the FBI investigation, which is expected to be completed before the Senate votes. Democratic Sens. Heidi Heitkamp (N.D.) and Joe Manchin III (W.Va.) also have yet to announce how they will vote.

If McConnell gets just two of those five senators, the result would be a 50-50 tie that would be broken by Vice President Pence, putting the 53-year-old Kavanaugh on the Supreme Court for life and shifting its balance of power to the right for a generation.

Republicans are under tremendous political pressure to deliver, with fears among party leaders that the GOP base will turn on them in next month’s midterm elections if they fail on Kavanaugh. Trump could nominate another conservative to fill the vacancy, but the Kavanaugh fight has increasingly become more about which side will win than about the nominee himself.

In that atmosphere, Republicans on the Judiciary Committee released an explicit signed statement they said had come from Dennis Ketterer, a onetime local TV weather forecaster in Washington, who wrote that he had a relationship in the 1990s with Julie Swetnick, the third woman who has accused Kavanaugh of misconduct. Swetnick has claimed that Kavanaugh was at a party where she was gang-raped in 1982 and that she had seen him try to get girls drunk at other parties so they could be raped.

Ketterer claims that Swetnick told him she enjoyed sex with multiple partners and that her father told him at one point that she had psychological problems.

Swetnick’s attorney, Michael Avenatti, dismissed the claims as “bogus and outrageous” and “absolutely fabricated to assist the GOP to ram through this nomination.”

Frustrated by Republican leadership’s handling of the nomination, Michael R. Bloomberg, the billionaire former mayor of New York who is considering a 2020 presidential run, is giving $20 million to the main Democratic Senate super PAC this week to help the party’s candidates.

A number of Kavanaugh’s former classmates have said he offered a misleading account to the Judiciary Committee about his conduct in high school and college that played down his excessive drinking, though it’s not clear whether all those people are being contacted by the FBI.

Ford’s team also has not heard back from the FBI, despite contacting the bureau repeatedly, according to her attorneys.

Ford’s testimony and the accounts from Kavanaugh’s former classmates, as well as more minor, seemingly implausible statements Kavanaugh made at last week’s hearing — like his benign explanations of references in his high school yearbook that could have more-sexual meanings — have led to increased Democratic attacks on his credibility.

“The greatest issue against Judge Kavanaugh, the one that bothers most people, is his credibility,” Minority Leader Charles E. Schumer (D-N.Y.) said Tuesday in a speech on the Senate floor. “Is he telling the truth? That issue supersedes all the others.”

“There are far too many misstatements, far too many inaccuracies, far too many mischaracterizations,” Schumer said.

Trump himself suggested Tuesday that if Kavanaugh lied to the Judiciary Committee, it would be disqualifying.

“I don’t think you can lie to Congress. There have been a lot of people over the last year that have lied to Congress, and, to me, that would not be acceptable,” Trump said.

Meanwhile, three former Kavanaugh clerks who had signed letters of support for him — Will Dreher, Bridget Fahey and Rakim Brooks — wrote in a letter to the Senate Judiciary Committee this week that they were deeply troubled by the allegations and expressed support for an “independent and thorough” investigation.

Two Yale Law School classmates who had endorsed Kavanaugh, Michael J. Proctor and Mark Osler, also pulled their backing, saying the judge’s testimony last week was “partisan, and not judicious.”

House Minority Leader Nancy Pelosi (D-Calif.) weighed in, saying at the Atlantic event that Kavanaugh was “hysterical” during the Senate hearing. She argued that yelling and crying by a woman would be viewed far differently.

Amid the back-and-forth, tensions ran high at the Capitol on Tuesday.

A small but vocal group of protesters gathered in the basement of the Russell Senate Office Building, running alongside every senator who walked through — most of them, Democrat or Republican, escorted by a Capitol Police officer.

Those who have declared they would vote against Kavanaugh, like Sen. Doug Jones (D-Ala.), got cheers and thank-yous. Those who have supported the nominee, despite the allegations against him, were challenged to remember sexual assault survivors — but the clamor of voices in the cavernous chamber made it difficult to hear the message through the din.

“This is dangerous,” said Sen. Lindsey O. Graham (R-S.C.), walking through the area with a Capitol Police officer and the deputy sergeant at arms, who yelled at protesters as Graham tried to talk to reporters. “I had somebody who wouldn’t let the elevator shut. Iraq War veteran, I appreciate his service, I just have a different opinion of Judge Kavanaugh and tried to make that clear.”

Graham said he wasn’t concerned that any senator other than Flake might waver on supporting Kavanaugh after they see the results of the FBI investigation.

But around the Senate, various Republicans were slightly hedging their bets.

Sen. John Neely Kennedy (R-La.) said he was still a yes on Kavanaugh but left open the tiniest of chances that the FBI’s findings could change his mind.

“My plan is to vote for Judge Kavanaugh, I said that last week, but that doesn’t mean I don’t want to see the results of the FBI report,” he said — refusing to guess whether the results would sway him.

Sen. Joni Ernst (R-Iowa), who has said she faced sexual harassment when she served in the military and has been an advocate for victims, said on CBS’s “This Morning” on Tuesday she will look at the FBI report for any evidence to corroborate Ford’s accusations.

“And if not, I will continue to support Judge Kavanaugh based on the information that I have at this time,” Ernst said. “We are innocent until proven guilty in this great country. . . . She has suffered from something very traumatic in her lifetime, but simply the corroboration wasn’t there.”

Hollie Askey, a 41-year-old Republican from the Des Moines area, welcomed Ernst’s support for Kavanaugh.

“The innocent-until-proven-guilty situation is just kind of out the window anymore, and I think it’s dangerous,” Askey said.

Amid the focus on Collins and Murkowski, Ernst is one of four other female Republican senators seen by leadership as solid votes for Kavanaugh. The others are Sens. Cindy Hyde-Smith (Miss.), Deb Fischer (Neb.) and Shelley Moore Capito (W.Va.). Capito is an alumna of the high school Ford attended, Holton Arms.

A new Quinnipiac Poll shows that a solid majority of women nationally oppose Kavanaugh’s nomination. But in the red states that Ernst, Hyde-Smith, Fischer and Capito represent, support for Trump runs high, and the senators have shown little sign of wavering in their backing of the nominee.

Indeed, Hyde-Smith, who was appointed to her seat in March and faces a primary in November, used her first-ever Senate floor speech last week to declare her staunch support for Kavanaugh, saying she was compelled to do so “by duty to our country and the people of Mississippi.”

And in West Virginia, if Democrat Manchin’s vote on Kavanaugh remains in doubt, Capito’s does not.

“It seems so partisan. I thought I had a shot at maybe changing Manchin’s mind,” said Catherine White, 66, a voter in Charleston, W.Va., who opposes Kavanaugh but emailed only Manchin’s office to say so. She said she would also try to contact Capito, as “I think she needs to hear from women.”

Alex Schuman in Des Moines, Zack Harold in Charleston and Seung Min Kim in Washington contributed to this report.