The allegation against Judge Kavanaugh, President Trump's pick for the United States top court, became public last week.
The lawyers said many aspects of Grassley's latest offer were "fundamentally inconsistent" with the committee's promise of a "fair, impartial investigation".
Grassley had said earlier that the panel would vote on Kavanaugh's confirmation on Monday unless a deal was reached with Ford's lawyers by a Friday night deadline.
"Dr. Ford will tell her story in the face of an impossible choice and vile bullying by Republican leadership", said Democratic Senator Richard Blumenthal of CT, a Judiciary Committee member.
Ford's accusations and the standoff over the terms of her appearance have left the appeals court judge's confirmation in jeopardy. Senate Majority Leader Mitch McConnell, R-Ky., has said that he has enough votes, but with at least two Republicans in the Senate undecided and with the party holding only a 51-49 majority, confirmation is hardly assured. I want to hear her.
But some Republicans believe the agreement to appear, sent just minutes before a 2:30 p.m. deadline set by Chairman Charles Grassley, is a smokescreen to delay a vote on the nominee.
The White House response shows a fresh willingness to attack Ford, coming after a series of critical comments from President Donald Trump the day before about her credibility.
Graham says Ford's lawyers are contesting two conditions for her testimony - that Ford and Kavanaugh will be the only witnesses and that an independent counsel will ask the questions.
"I will listen if she does". In tweet Friday, Trump broke his silence to cast doubt on Ford's story in ways Republicans had been carefully trying to avoid.
The Senate Judiciary Committee confirmed that the next Kavanaugh nomination hearing has been rescheduled to Thursday at 10am (2pm Irish time). Kavanaugh and his wife also had received threats, a senior White House official said. Kavanaugh, who has vigorously denied the allegations, has repeatedly expressed his desire to testify.
Ford's husband, Russell Ford, was quoted by The Post on Saturday as saying the thought Kavanaugh could be considered for the Supreme Court after Trump took office troubled her so much that she considered moving as far away as New Zealand.
The question of whether Ford would testify before the committee had gone unanswered for several days 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.
Republicans had hoped to push through a successful confirmation of the president's pick to join the Supreme Court before oral arguments begin on October 1.
Earlier on Saturday, vice president Mike Pence called Mr Kavanaugh "a man of integrity with impeccable credentials". At this point, only the power of her testimony may be able to affect the outcome of Kavanaugh's nomination for a seat on the highest court.
Mark Judge, the friend who was allegedly in the room with Kavanaugh and Ford, denied having any recollection of the party.
The Post reported Sunday that Keyser said in a brief interview at her home that she still believes Ford, even if she doesn't remember the party.
"I think Dr. Ford has come forward understanding what she was going to face", Sen.