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Vice President Mike Pence on Tuesday said that Senate Democrats should meet with Supreme Court nominee Amy Coney Barrett as she prepared to meet with several Republican senators -- and as several Democrats have said they will refuse to meet with Barrett, calling her nomination "illegitimate."

Barrett on Capitol Hill Tuesday is meeting with Pence and Senate Majority Leader Mitch McConnell, R-Ky., to begin her day and closing in a meeting with Senate Judiciary Committee Chairman Lindsey Graham, R-S.C. She will also meet with Sens. John Thune, R-S.D., Ted Cruz, R-Texas; Chuck Grassley, R-Iowa; Rick Scott, R-Fla.; Mike Crapo, R-Idaho; Mike Lee, R-Utah; and Cory Gardner, R-Colo.

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"We have someone of great character, of great intellect, who has a judicial philosophy that will uphold the Constitution of the United States," Pence said in a brief statement to reporters. "We look forward ... to working with ... Republicans in the Senate and we hope the Democrats in the Senate as well as you discharge your duty to advise and consent."

Pence added: "We believe the Senate has an opportunity ... for a fair and respectful consideration, a hearing, we urge our Democrat colleagues in the Senate to take the opportunity to meet with Judge Barrett and as the hearing goes forward to provide the kind of respectful hearing that the American people expect."

Barrett did not make any comments. McConnell briefly spoke, saying he was happy to get the confirmation process underway.

"We're pleased today to welcome Judge Barrett to begin the process of advice and consent in the Senate," the majority leader said. "And as you know she’ll be visiting with members who are interested in talking to her during the course of the next few days. And we’re glad to have her here and get the process started."

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A reporter asked if Barrett should recuse herself from any election-related case as Pence wrapped his remarks -- what would be an unprecedented move for a Supreme Court justice with no clear justification besides that Trump nominated her -- and nobody answered.

Several Democratic senators have said that the Barrett confirmation process is "illegitimate," including Senate Minority Leader Chuck Schumer, D-N.Y., and Sens. Richard Blumenthal, D-Conn., Maize Hirono, D-Hawaii, Kirsten Gillibrand, D-N.Y., and Bob Casey, D-Pa.

"I believe first the whole process has been illegitimate," Senate Minority Leader Chuck Schumer, D-N.Y., said on Sunday. "And second, because she's already stated that she is for overturning the ACA. I will not meet with her."

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Schumer has also said that Republicans "will have stolen two Supreme Court seats" in four years -- a reference to the seat Justice Neil Gorsuch currently occupies after Republicans held it open for months ahead of the 2016 presidential election. Republicans have defended the move, noting that historically election-year vacancies have been filled when the Senate and president are of the same party and left open when they are not.

But filling a Supreme Court vacancy just weeks ahead of a presidential election is still a remarkable move compared to modern precedent.

The Senate last confirmed a justice during an election year with Justice Frank Murphy in January 1940. Before that, it confirmed Justice Benjamin Cardozo in February 1932 and Justice Louis Brandeis in January 1916.

Fox News' Chad Pergram contributed to this report.