The White House says it would welcome Senate testimony from Brett Kavanaugh's second accuser, Deborah Ramirez, who says he exposed himself to her at a Yale University party in the 1980s. Ramirez' attorney, John Clune, said his client is "willing" to testify and that the gaps in her memory only strengthen her credibility.

Clune contacted Republican Senate aides this week about his client testifying but the GOP asked for written details from Ramirez about any witnesses or evidence before they speak on the phone. Clune wants to talk before handing anything over.

"She would be willing to testify, but she wants…us to be able to have this conversation about what this is going to look like, what the process is going to be and if there's going to be an FBI investigation into what happened in her case," Clune told "CBS This Morning" on Wednesday.

Ramirez has admitted that she doesn't remember all the details from the night in question and reportedly said she can't be absolutely sure it was Kavanaugh who exposed himself to her. He believes that only helps her case.

"If somebody's going to make something up they're not going to put gaps in their memory, right? She was very, very conscientious about only putting forth the information that she was comfortable with and acknowledging the things that were the gaps in her memory. So that -- as a former prosecutor, I can tell you that only helps her credibility because somebody's not going to falsify a report that has that kind of gap," Clune said.

According to Clune, they had a call set up last night with Republicans on the Judiciary Committee but only Democrats joined the call.

"They say they want conditions in place before they'll talk with us on the phone. They want us to send them all the information that we have for their consideration before they'll talk to us for whatever reasons," Clune said.

CBS News correspondent Nancy Cordes asked Judiciary Committee communications director Taylor Foy why the committee's chief counsel was unwilling to have a phone call with Ramirez' lawyers before they hand over their evidence in writing first.

He responded, "As a matter of course our investigators want to be able to review a statement or evidence first in order to determine how best to proceed. That sort of information can help inform discussions in future phone calls or meetings."

Christine Blasey Ford, the first woman to come forward and accuse Kavanaugh of sexual misconduct, will testify along with Kavanaugh in a public hearing Thursday.

The Supreme Court nominee has denied all allegations and could be facing a third accuser before Ford's testimony. Attorney Michael Avenatti says he has a client who knew Kavanaugh in high school and accuses him of setting up girls to be raped. He has not identified the accuser yet but said that her name will be revealed before Thursday.