Bolstered by a new memo questioning the reliability of Brett M. Kavanaugh’s chief accuser, Republican leaders on Monday set a firm deadline for the FBI to finish its investigation and for the Senate to vote this week on elevating Judge Kavanaugh to the Supreme Court.

The memo, written by the sex-crimes prosecutor Republicans hired to question Christine Blasey Ford and Judge Kavanaugh at last week’s dramatic hearing, points to numerous inconsistencies and lack of corroboration for Ms. Blasey Ford’s account of the sexual assault she says she suffered when they were in high school 36 years ago.

Rachel Mitchell, the prosecutor, said not only wouldn’t she bring a criminal case based on Ms. Blasey Ford’s account, but she also doubts it would even be a winning case in a civil suit, where the standards of proof are lower.

Ms. Mitchell said the case is even weaker than “he-said, she-said” because it’s completely uncorroborated.

Her memo says Ms. Blasey Ford’s accounts have changed from her initial tip to The Washington Post in early July to a letter she wrote to Sen. Dianne Feinstein, California Democrat, in late July to her interview with The Post in September and then her testimony. That includes a shifting date for the house party where she says the sexual assault occurred, as well as the number and genders of other people she says were at the gathering.

“Dr. Ford has struggled to recall important events relating to her allegations, and her testimony regarding recent events raises further questions about her memory,” Ms. Mitchell concluded.

With the FBI now investigating, Democrats said they want not only Ms. Blasey Ford’s allegations but also those of two other women who have accused Judge Kavanaugh of sexual misconduct to be examined. They have suggested at least two dozen people they say should be interviewed before the FBI wraps up its investigation.

President Trump, speaking at the White House, said he has asked the FBI to look at any allegation “within reason,” but he added that it must be done quickly because ambush accusations are unfair to Judge Kavanaugh.

Republican leaders in the Senate agreed and said they will soon force final action.

“The time for endless delay and obstruction has come to a close. Judge Kavanaugh’s nomination is out of committee. We’re considering it here on the floor,” said Senate Majority Leader Mitch McConnell, Kentucky Republican. “We’ll be voting this week.”

It was not clear what that meant for the FBI and for timing of a final vote.

Under Republicans’ original plans, Judge Kavanaugh was to be sitting on the high court Monday morning, when the justices’ 2018-2019 term began.

Instead, lawmakers delayed a committee vote after Ms. Blasey Ford’s allegations surfaced. Then, after powering the nomination through the panel on Friday, Republicans agreed to put off a floor vote while the FBI investigated. That delay is supposed to last one week.

Democrats said timing is less important than thoroughness. They have asked that the FBI interview Ms. Blasey Ford, Deborah Ramirez, who says the judge exposed himself to her at a college party in the 1980s, and Julie Swetnick, who has said she suspects the judge may have been involved in gang rapes at high school parties in the early 1980s, though she cannot be more definitive.

Also topping the list of people they say should be interviewed is Mark Judge, a friend of Judge Kavanaugh’s from his high school days. Ms. Blasey Ford says Mr. Judge was in the bedroom at the house party and ended the assault when he jumped on top of her and Judge Kavanaugh.

Mr. Judge’s attorney said Monday that Mr. Judge was interviewed by the FBI but that interview wasn’t complete.

Senate Minority Leader Charles E. Schumer of New York said Democrats want to see a full list of parameters that the FBI has been given for its investigation, fearing Republican attempts to circumscribe the investigation. He said agents must brief senators on what they learned before the Senate takes any final vote on Judge Kavanaugh.

“Whether you are for or against Judge Kavanaugh going to the Supreme Court, it will only benefit the country if the investigation is regarded as fair, clear and not constrained, particularly by partisan means,” Mr. Schumer said. “Democrats are not interested in delay for the sake of delay. This can all be completed quickly, but it must be done right.”

Mr. McConnell said he doubted Democrats, most of whom said they opposed Judge Kavanaugh well before there was any hint of sexual assault allegations, will ever be satisfied. He predicted they would oppose Judge Kavanaugh for his acknowledged affinity for beer, or his indignant denunciations at last week’s hearing of the accusations against him — and Democrats’ treatment of him.

“Their goal posts are shifting,” Mr. McConnell said.

Republican senators said they are not sure whether they have the votes to confirm Judge Kavanaugh and that the FBI’s report will be the determining factor.

They said the public will have to be informed about what the FBI finds.

“There is going to have to be some sort of announcement about what this supplemental investigation has yielded, I think, because now these allegations have been made so far unproven,” said Sen. John Cornyn of Texas, Mr. McConnell’s top lieutenant.

If Democrats’ goal posts are shifting, so is public opinion.

The latest Quinnipiac University poll showed 48 percent of voters said Judge Kavanaugh shouldn’t be confirmed, up 6 percentage points since the previous Quinnipiac poll. Voters believe Ms. Blasey Ford over Judge Kavanaugh 48 percent to 41 percent.

Both Democrats and Republicans called her testimony last week compelling.

She said she was “100 percent” certain it was Judge Kavanaugh, a student at a neighboring high school, who pushed her into a room during a party, groped her, attempted to strip off her clothes and stifled her cries for help. She testified that she remembered him and Mr. Judge laughing at her, both during and after the assault, “pinballing” off the hallway walls while returning to the party.

Ms. Mitchell, the sex-crimes prosecutor, said in her memo to senators that the case was not so compelling.

Ms. Mitchell pointed out that Ms. Blasey Ford “struggled to identify Judge Kavanaugh” by name until decades after the attack. Neither the couples therapy notes from 2012 where she says she first identified Judge Kavanaugh, nor individual therapy notes from 2013 contained the name, Ms. Mitchell said.

Russell Ford, Ms. Blasey Ford’s husband, told The Post that he remembers his wife identifying Judge Kavanaugh during their 2012 therapy.

But Ms. Mitchell questioned that, saying Judge Kavanaugh’s name was in the news at the time as a potential Supreme Court pick for Republican presidential nominee Mitt Romney.

Ms. Mitchell also questioned the validity of the polygraph exam Mr. Blasey Ford arranged to take in August and wondered about the woman’s motivations for coming forward in the manner she did. The prosecutor also suggested that Ms. Blasey Ford’s account was likely affected by pressure from her attorneys and from Senate Democrats.

While those conclusions echo Republicans’ takeaways from the hearing, Ms. Mitchell said she wrote the memo and her thoughts were not dictated or influenced by anyone.

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