The senate committee looking into Mr Kavanaugh's confirmation has invited Professor Blasey Ford to give evidence on Monday, but she says she wants an FBI investigation into her allegations first.
Some Republicans in the Senate are already stepping onto treacherous terrain by suggesting that Ford is "mixed up" or "confused".
Grassley had said that in the interest of making Ford comfortable, he'd be willing to let Ford testify in public or private.
Ford's lawyers say she has been the target of "vicious harassment and even death threats" since coming forward with her story.
Several hours after posting her tweet, she deleted it, and when asked about why she deleted it, she responded: "Hi all, deleted this because it served its goal and I am now dealing with a slew of requests for interviews from The Wash Post, CNN, CBS News".
"The rush to a hearing is unnecessary, and contrary to the Committee discovering the truth".
Ms Blasey Ford claims Judge Kavanaugh sexually assaulted her when they were teenagers.
Ford said Kavanaugh was "stumbling drunk" during a small party in high school, at which he pinned her to a bed, groped her over her clothes, and covered her mouth with his hand when she started to scream. "Nothing the Federal Bureau of Investigation or any other investigator does would have any bearing on what Dr Ford tells the committee, so there is no reason for any further delay", Grassley said in a statement.
This former classmate, Cristina King Miranda, in a Facebook post she later deleted, claimed on Tuesday that she knew Ford, Kavanaugh's accuser, in school and that everyone knew about the alleged incident.
Democrats have called on the Senate Judiciary Committee to postpone its vote until the allegations are investigated.
The duelling testimony had been expected to take place Monday in a piece of blockbuster Washington theatre, putting both Trump's bid to tilt the Supreme Court to the right and political momentum ahead of November midterm congressional elections into play.
Ford wants an FBI investigation done before testifying, but President Donald Trump and Republicans have rebuffed her.
Republicans are rejecting Ford's call for an FBI investigation, putting the onus back on her to decide whether she'll testify anyway.
It remained unclear, though, whether Ford would attend or if the hearing would occur without her as a drama that has riveted Washington since emerging a week ago was injected with a fresh burst of election season suspense.
Dozens of protesters, a lot of them women, clogged the lobby of Grassley's Senate office on Thursday. "It is my understanding that Dr. Ford has been represented by counsel in this matter for months and thus should be adequately prepared to testify", Grassley wrote.
They asked to speak to Grassley and were told the senator is in Iowa, according to Marcie Wells of Las Vegas, a member of the Women's March organization that has been outspoken in opposition to Kavanaugh's nomination. The allegation has jarred Kavanaugh's prospects for winning Senate confirmation to be a justice, which until Ford's emergence last week had seemed all but certain.
Grassley did not immediately respond to Katz's demands.
One of the four has yet to be publicly identified.
"Dr. Ford was reluctantly thrust into the public spotlight only two days ago", Ford's attorney said in a statement Wednesday.
Republicans say Ford will have one chance to testify, and one chance only.