Washington (CNN) Christine Blasey Ford said in a letter Tuesday that she wants an FBI investigation into her allegation of sexual assault against Supreme Court nominee Brett Kavanaugh before the Senate holds a hearing on her allegations.

The letter, obtained by CNN, capped off a day of uncertainty around the planned hearing for Monday morning, which Senate Judiciary Committee Chairman Chuck Grassley had said he would hold to hear from both Ford and Kavanaugh, who denies the allegations.

Ford's attorney Lisa Banks told Anderson Cooper on "CNN's Anderson Cooper 360" that Ford will talk with the committee but added, "She is not prepared to talk with them at a hearing on Monday."

"She will talk with the committee," Banks said. "She is not prepared to talk with them at a hearing on Monday. This just came out 48 hours ago."

"Asking her to come forward in four or five days and sit before the Judiciary Committee on national TV is not a fair process. If they care about doing the right thing here and treating this seriously as they have said, then they will do the right thing and they will properly investigate this, and she will work with them in that investigation and also to share her story with the committee," Banks said Tuesday night.

Senate Majority Leader Mitch McConnell said Tuesday evening that Republicans still had not heard from Ford or her attorney regarding an invitation to testify before the Senate Judiciary Committee next week.

Republican sources on Capitol Hill say it's uncertain if the hearing scheduled for next Monday to address the accusation against Kavanaugh will occur.

Grassley, an Iowa Republican, had said Tuesday morning that he had yet to hear back from Ford, who says Kavanaugh sexually and physically assaulted her while they were both in high school.

Grassley told Hugh Hewitt on his radio show that Ford has not accepted his request to appear before the committee.

"We have reached out to her in the last 36 hours, three or four times, by email, and we have not heard from them," Grassley said. "So it kind of raises the question, do they want to come to the public hearing or not?"

McConnell said Tuesday that the committee has yet to decide on the makeup of the hearing, and added that they would offer her the opportunity to speak privately if she preferred.

Utah GOP Sen. Orrin Hatch said on Tuesday evening that they planned to proceed with the nomination even if Ford does not show up at the planned hearing on Monday.

"We're going to proceed -- there's no question about it," Hatch said.

Sen. Jeff Flake, R-Arizona, sits on the Judiciary Committee and had previously said the committee should hold off on voting until they hear from the accuser. However, Flake said Tuesday that if Ford fails to appear at the hearing scheduled for Monday, he would support his party's push to move forward on a vote on Kavanaugh.

"I think we'll have to move to the markup," he told CNN.

Flake said he's hopeful Ford will accept the committee's invitation and speak at the hearing. "I hope she does. I think she needs to be heard," he said.

Ford, in the letter via her attorneys, said she faced "vicious harassment and even death threats" since she came forward and still wanted to cooperate with the committee and law enforcement.

"We would welcome the opportunity to talk with you and Ranking Member (Dianne) Feinstein to discuss reasonable steps as to how Dr. Ford can cooperate while also taking care of her own health and security," the letter from Ford's lawyers said.

Garrett Ventry, a spokesman for the Senate Judiciary Committee, said Grassley condemned the threats.

"Chairman Grassley condemns these threats toward Dr. Blasey. He looks forward to a fair, respectful, and thorough hearing next week," Ventry said in a statement before the letter was released.

Earlier Tuesday, upon entering McConnell's office, Hatch told reporters that lawmakers were meeting to figure out the next steps -- including whether the hearing would proceed without Ford.

Flake also met with leadership at around noon on Tuesday to talk about a possible delay in the nomination process in order to schedule a hearing so Ford could tell her story. Flake said some Republicans wanted to push for a hearing on Thursday, but he insisted on Monday.

Sen. John Cornyn, R-Texas, called Ford's silence "pretty telling," but added they hope she does testify.

"That's pretty telling, she hasn't responded to the committee's normal processes and we don't know if she's coming or not but this is her chance. This is her one chance. We hope she does," Cornyn said.

Democrats maintain that they want the FBI to reopen Kavanaugh's background check ahead of a hearing.

The 10 Democrats on the Senate Judiciary Committee penned a letter to FBI Director Christopher Wray and White House Counsel Don McGahn on Tuesday arguing that the FBI needs to complete an investigation before the hearing is scheduled to take place on Monday.

"The Committee should have the completed report before any hearing occurs and we ask that you take immediate steps to make sure that we have the FBI's report before we proceed," the senators wrote.

If the FBI doesn't investigate the allegation, said Sen. Feinstein of California, the top Democrat on the judiciary panel, she thinks the hearing should be delayed.

"The important thing is to get this investigated," Feinstein said. "There was a witness there -- and that was this fellow (Mark) Judge. ..."

Republican Sen. Susan Collins of Maine, a key Senate vote on Kavanaugh's nomination, said it would be "puzzling" if Ford did not testify on Monday.

"That's very puzzling to me," she said about the uncertainty of Ford's appearance. "I've said from the beginning that these are very serious allegations and she deserves to be heard. She is now being given an opportunity to come before the Senate Judiciary Committee to answer questions, and I really hope that she doesn't pass up that opportunity."

When asked about Democrats' request for the FBI to reopen its background investigation of Kavanaugh before the hearing takes place -- and whether that could be a deciding factor for Ford to testify, Cornyn said: "She is not really in a position to make conditions, in my view."

Since Kavanaugh was first nominated, Republicans have continued to emphasize the importance of following the proper procedures -- a message President Donald Trump has even touched on since the accusation came to light.

However, Feinstein's request for an investigation ahead of the hearing breaks with procedure. She also has questioned the speed of the hearing and the fact that there will be only two witnesses, Kavanaugh and Ford.

But a source who supports Kavanaugh notes that it was Feinstein who declined to release the letter back in July before the hearings, and rejects any notion that the FBI should step in and investigate first.

"That's not how it works," he said.

"The hearing is the investigation. At the heart of the investigation is what Ford says. If Ford doesn't want an investigation than she shouldn't have gotten into this game in the first place," he said.

CORRECTION: This story has been updated to correct when Senate Judiciary Chairman Chuck Grassley made his comments about not hearing back from Christine Blasey Ford. It was Tuesday.