High court nominees traditionally meet with senators of both parties ahead of their confirmation hearing in the judiciary committee. For this nomination, however, some Democrats have said they don't plan to participate because they believe the winner of the Nov. 3 election should pick Justice Ruth Bader Ginsburg's successor.
"I am not going to meet with Judge Barrett," Senate Democratic leader Chuck Schumer tweeted Tuesday morning. "Why would I meet with a nominee of such an illegitimate process and one who is determined to get rid of the Affordable Care Act?"
McConnell -- who's pushed for Barrett's confirmation hearings, despite not allowing any action for former President Barack Obama's nominee in 2016 after Justice Antonin Scalia's death -- called for Democrats to participate in the full confirmation process.
"We believe the Senate has an opportunity here for a fair and respectful consideration," Pence said ahead of the meeting. "We urge our Democratic colleagues int he Senate to take the opportunity to meet with Judge Barrett, and as the hearing goes forward to provide the kind of respectful hearing the American people expect."
Trump nominated Barrett on Saturday, a little over a week after Ginsburg died. If confirmed, she would be his third appointment to the Supreme Court since he took office in 2017 -- following Neil Gorsuch and Brett Kavanaugh.
"This should be a straightforward and prompt confirmation. This should be very easy. It should be very quick. I'm sure it will be extremely non-controversial. We said that last time, didn't we?" Trump said of Barrett's nomination last weekend.
Democrats have taken issue with Trump nominating the next justice less than two months ahead of the presidential election. McConnell blocked hearings on the confirmation of Merrick Garland -- Obama's nominee four years ago -- because he and other GOP senators said the next elected president should select Scalia's replacement.
Scalia, for whom Barrett clerked at one time, died some nine months before the 2016 election.
Barrett, 48, who serves on the 7th U.S. Circuit Court of Appeals, is a devout Catholic who opposes abortion. Should she be confirmed, she would give the court an even greater conservative majority at 6-3.
Ginsburg died of cancer at age 87 on Sept. 18. She had served on the high court since 1993 and became widely known as a fighter for gender equality.
Barrett's confirmation hearing is scheduled to begin Oct. 12.