Smash Racism D.C. shared two videos from the protesters around 10 p.m. as the group chanted at the Texas senator, "We believe survivors."
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One man can be heard saying, "Beto is way hotter than you, dude!" Rep. Beto O'Rourke, Texas Democrat, is running against Mr. Cruz for Senate.
A woman shouts, "Ted Cruz and Brett Kavanaugh are best friends!"
The first video captures a woman identifying herself as a constituent and sexual assault survivor and asking Mr. Cruz how he would vote on Judge Kavanaugh.
"I have a right to know what your position is on Brett Kavanaugh," the woman said.
SEE ALSO: Houston Councilwoman Ellen Cohen recounts her own sexual assault while weighing in on Kavanaugh allegations
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She stressed that she knew that the two were close and wanted to know if Mr. Cruz had talked with Judge Kavanaugh about the allegations against him.
"There are people now that have come forward and who have said Brett Kavanaugh has attacked them," she said.
RELATED: Supreme Court nominee Brett Kavanaugh's Yale roommate says he believes second accuser
Judge Kavanaugh was first accused of sexual assault by California professor Christine Blasey Ford who came forward more than a week ago. She claims that he was "stumbling drunk" when he trapped her in a bedroom and assaulted her at a party while they were both in high school. She and Judge Kavanaugh will testify about the allegations on Thursday.
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A second accuser, Deborah Ramirez, came forward on Sunday. In a New Yorker article, Ms. Ramirez alleged that Brett Kavanaugh exposed himself to her at a party in their freshman dorm when they attended Yale.
Michael Avenatti, known for his representation of porn star Stormy Daniels, claims he is representing a third woman. He has floated some explicit claims on Twitter and demanded that the Senate Judiciary Committee allow his client to testify at the hearing Thursday.
Mr. Avenatti's client has not come forward publicly yet. The only information he's shared is that she has information about Judge Kavanaugh's high school conduct and she worked in the federal government for years.
Judge Kavanaugh has denied all allegations against him.
"I'm not going to let false accusations drive us out of this process, and we're looking for a fair process where I can be heard and defend my integrity, my lifelong record," he said in an interview on Fox News Monday night. "My lifelong record of promoting dignity and equality for women starting with the women who knew me when I was 14 years old. I'm not going anywhere."