Members of the Senate Judiciary Committee and attorneys for Christine Blasey Ford have tentatively agreed to hold a public hearing Thursday so that she can share details of her accusations, according to multiple Democrats and Republicans familiar with the plans. Ford has accused Supreme Court nominee Brett Kavanaugh of sexually assaulting her 36 years ago.

A "short but very productive call" between Democratic and Republican members of the committee and Ford's attorneys yielded the agreement, according to one person familiar with the call.

All sides plan to speak again Sunday to sort out final details.

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"There was a very productive discussion tonight and it looks like they're down to the final details. But, the devil is in the details. I'm not saying it's a done deal," said another person familiar with Saturday's exchanges. "It looks like it will be Thursday, but [Judiciary Committee Chairman Chuck] Grassley has to run it by his people."

Late Saturday, an attorney for a woman believed to be one of the witnesses Ford said was at the party released a statement to the Senate Judiciary Committee and CBS News denying she was at the party. An attorney for the woman, Leland Keyser, said in the statement "simply put, Ms. Keyser does not know Mr. Kavanaugh and she has no recollection of ever being at a party or gathering where he was present, with, or without, Dr. Ford."

In a response, Ford's attorney, Debra Katz, called it "not surprising" that Keyser did not recall the party.

"As Dr Ford has said, she did not share her story publicly or with anyone for years following the incident with Judge Kavanaugh," Katz said in a statement. "It's not surprising that Ms. Keyser has no recollection of the evening as they did not discuss it. It's also unremarkable that Ms. Keyser does not remember attending a specific gathering 30 years ago at which nothing of consequence happened to her. Dr. Ford of course will never forget this gathering because of what happened to her there.

Before the agreement had been announced, Ford's lawyers said she had agreed to "provide her first-hand knowledge of Brett Kavanaugh's sexual misconduct next week."

Ford's attorneys and Grassley have been publicly ironing out whether she will testify about the alleged incident since Friday, when Grassley demanded a decision on whether she would testify by 10 p.m. Her lawyers responded with a public request for one more day, and Grassley tweeted shortly before midnight that they had granted the extension.

Michael Bromwich, former inspector general of the Justice Department, announced Saturday that he joined Ford's legal team.

I’m honored to be joining Debra Katz and Lisa Banks in representing Dr. Ford https://t.co/WdhWj0qmSw — Michael R. Bromwich (@mrbromwich) September 22, 2018

Grassley had requested that Ford respond to his invitation to testify before the Senate by Saturday afternoon. Republican committee staff and Ford's lawyers had reached a stalemate in negotiations over the details of the testimony.

Although Democratic committee staff members usually would participate in these negotiations, Democrats are refusing to do so because they believe that the investigation into the allegations should be conducted by the FBI.

Republicans on the committee and Ford's lawyers had disagreed on numerous counts. Katz requested that the hearing be held next Thursday, and that Kavanaugh testify before Ford, among other requests. Republicans made a counteroffer Friday of holding the hearing Wednesday, and having Ford testify before Kavanaugh.

CBS News' Ed O'Keefe, Jan Crawford and Caroline Linton contributed reporting.