The vote will take place a day after Kavanaugh and Christine Blasey Ford testify before senators about sexual assault allegations.
Ford accused the judge of forcing himself on her at a party when they both were in high school in the early 1980s.
Judiciary Chairman Sen. Chuck Grassley, R-Iowa, confirmed the committee hired outside counsel Rachel Mitchell, who will ask questions for Republican senators during the hearing. Democrats will conduct their own questioning.
Mitchell is on leave from her role as deputy county attorney in the Maricopa County Attorney's Office, where she is also chief of the special victims division, Grassley said Tuesday night.
"I promised Dr. Ford that I would do everything in my power to avoid a repeat of the 'circus' atmosphere in the hearing room that we saw the week of Sept. 4," Grassley said. "I've taken this additional step to have questions asked by expert staff counsel to establish the most fair and respectful treatment of the witnesses possible."
Senate Majority Leader Mitch McConnell said he didn't believe men should be disqualified from the process, but praised the presence of outside counsel.
"We want this hearing to be handled very professionally, not a political sideshow like you saw the -- put on by the Democrats when they were questioning Judge Kavanaugh," he said.
The White House said Tuesday it is open to the possibility of a second woman who's accused Kavanaugh of sexual assault testifying in the Senate.
The second woman, Deborah Ramirez, came forward in an article in The New Yorker magazine Sunday, saying Kavanaugh exposed himself to her while they were attending Yale University in the 1983-84 academic year.
Sanders' comments came hours after Kavanaugh appeared on Fox News.
"What I know is the truth, and the truth is I've never sexually assaulted anyone," Kavanaugh told Fox News in an interview with Martha MacCallum that aired at 7 p.m. Monday on The Story.
The judge's wife, Ashley Kavanaugh, joined the interview and said the accusations are "hard to believe."
"I know Brett. I've known him for 17 years. He's decent, he's kind, he's good. I know his heart. This is not consistent with Brett," she said.
At the U.N. General Assembly in New York City on Tuesday, President Donald Trump told reporters he questions Ramirez's story, saying she was drunk and said there are lapses in her version of events. He also again blamed the row on Democrats, saying they only want to "resist and obstruct" to derail Kavanaugh's appointment.
"I think he is just a wonderful human being. I think it is horrible what the Democrats have done. It is a con game, they are really con artists," he said.
"He is one of the highest quality people. He said when he was focused on being No. 1 in his class at Yale, to me, that was so believable."
Kavanaugh, a judge on the U.S. Court of Appeals, was appointed by Trump to succeed Justice Anthony Kennedy, who retired this summer. Ford has accused Kavanaugh of assaulting her at a high school party in 1982, saying he held her down, covered her mouth and tried to remove her clothes.
Avenatti said he's been hired by a former State Department and U.S. Mint employee with multiple security clearances who has new accusations about Kavanaugh and his high school friend, Mark Judge.
"It will relate to how they behaved at countless house parties," Avenatti said.
She's "literally risking her life" by coming forward and she is "100 percent credible" with multiple witnesses, he said. She's prepared to take a polygraph test if Kavanaugh also does.
Trump reiterated his support for Kavanaugh in a tweet Monday night.
"The Democrats are working hard to destroy a wonderful man, and a man who has the potential to be one of our greatest Supreme Court Justices ever, with an array of False Accusations the likes of which have never been seen before!" Trump said.
Brett Kavanaugh's confirmation hearings for Supreme Court