Attorneys for Christine Ford, the California professor accusing Supreme Court nominee Brett Kavanaugh of sexually assaulting her in high school, definitively vowed Sunday that Ford would appear at a Senate hearing Thursday morning despite unresolved "procedural and logistical issues."

After nearly a week of uncertainty, the move sets the stage for a dramatic and pivotal day of testimony on Capitol Hill that could determine the fate of President Trump's second pick to the nation's highest court.

"We made important progress on our call this morning with Senate Judiciary Committee staff members," the attorneys, Debra Katz, Lisa Banks, and Michael Bromwich said in the statement. "We committed to moving forward with an open hearing on Thursday Sept 27 at 10:00 am."

Sources on Capitol Hill tell Fox News they are now preparing in earnest for the Thursday hearing, which is likely to push a confirmation vote on the Senate floor beyond October 1, the start of the next Supreme Court term.

The hearing had been in doubt amid protracted back-and-forth tussling between Senate Republicans and Ford's legal team, who disagreed on the ideal timing of the hearing, as well as who should testify first and whether outside lawyers should be allowed to ask questions.

But Ford's legal team said categorically on Sunday that those potential sticking points would not derail the hearing.

WATCH: LINDSEY GRAHAM RIPS DEMS FOR 'USING' KAVANAUGH ACCUSER

"Despite actual threats to her safety and her life, Dr. Ford believes it is important for Senators to hear directly from her about the sexual assault committed against her," the attorneys said. "She has agreed to move forward with a hearing even though the Committee has refused to subpoena Mark Judge. They have also refused to invite other witnesses who are essential for a fair hearing that arrives at the truth about the sexual assault.

"A number of important procedural and logistical issues remain unresolved, although they will not impede the hearing taking place," the attorneys added. "Among those issues is who on the Majority side will be asking the questions, whether senators or staff attorneys."

The legal team concluded: "We were told no decision has been made on this important issue, even though various senators have been dismissive of her account and should have to shoulder their responsibility to ask her questions. Nor were we told when we would have that answer or answers to the other unresolved issues. We look forward to hearing back from the Majority staff as soon as possible on these important matters."

Kavanaugh will reportedly testify after Ford, allowing him the opportunity to respond to her claims.

WATCH: TOP DEMOCRAT SAYS KAVANAUGH'S CONSERVATIVE LEGAL PHILOSOPHY IS A REASON TO DENY HIM DUE PROCESS

Judge, who Ford has said was in the room when she was allegedly assaulted by Kavanaugh, had indicated he did not want to testify because he had nothing to add beyond his denial of any knowledge of the purported episode. Republican senators had said it would be inappropriate for a witness to dictate who would be called.

Speaking on "Fox News Sunday," Sen. Lindsey Graham, R-S.C., a member of the Judiciary Committee, said that there would be two witnesses: Kavanaugh and Ford.

That would mark a change from the 1991 Judiciary Committee hearings into allegations by Anita Hill that she had been sexually harassed by then-Supreme Court nominee Clarence Thomas. Several witnesses testified in those nationally televised proceedings, which saw Thomas fervently deny the allegations that he compared to a "hi-tech lynching."

All of the individuals that Ford has said were at the house during the alleged assault -- including Kavanaugh, Judge, classmate Patrick Smyth, and her own longtime friend, Leland Ingham Keyser -- have denied knowledge of the episode, under penalty of felony, in interviews with the Judiciary Committee.

Ford has said she does not recall who owned the house where the alleged attack occurred, nor why there was a gathering there or exactly when the incident occurred.

"If she wanted to stay anonymous, those who betrayed her need to apologize." — Sen. Lindsey Graham, R-S.C.

For their part, Democrats have repeatedly accused Republicans of pressuring Ford to appear before the Senate Judiciary Committee. Sen. Dianne Feinstein, D-Calif., has said Ford, who lives in California and has received numerous death threats, shouldn’t “be rushed" in her decision of when to testify.

“Show some heart,” Feinstein said. “Wait until Dr. Ford feels that she can come before the committee.”

WATCH: FEINSTEIN ADMITS SHE CAN'T BE SURE ACCUSER BEING ENTIRELY 'TRUTHFUL'

But Feinstein herself has come under fire from Republicans because she received a letter from Ford outlining her allegations on July 30, but only discussed them with other senators and federal authorities less than two weeks ago. Her disclosure was prompted by a leak describing the letter in The Intercept -- a leak that Republicans have charged was orchestrated by Democrats.

Senate Judiciary Committee Chairman Chuck Grassley, in a letter last week, unloaded a torrent of criticism on Feinstein for delaying the disclosure, saying she had compromised Ford's anonymity and used a sexual assault allegation for political gain.

"I cannot overstate how disappointed I am," Grassley wrote.

On Sunday, Graham echoed that sentiment.

"I feel sorry for her," Graham told "Fox News Sunday," referring to Ford. "I think she's being used here. If she truly wanted to be anonymous, the person who brought this allegation to the public owes her an apology."

He added: "I don’t know what Dr. Ford expected us to do with an anonymous letter. If she wanted to stay anonymous those who betrayed her need to apologize."

Fox News' Shannon Bream and Chad Pergram contributed to this report.