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Supreme Court nominee Judge Amy Coney Barrett is set to start meeting with senators on Tuesday as her accelerated confirmation process continues despite multiple Democrats refusing to see her, calling the process that led to her nomination so close to a presidential election "illegitimate."

"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."

Schumer, who has said if Barrett is confirmed the GOP "will have stolen two Supreme Court seats," is joined by Sens. Richard Blumenthal, D-Conn., and Maize Hirono, D-Hawaii, in refusing to meet with the 7th U.S. Circuit Court of Appeals judge. "I will oppose the confirmation of Judge Amy Coney Barrett, as I would any nominee proposed as part of this illegitimate sham process, barely one month before an election as Americans are already casting their votes," Blumenthal said Sunday.

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Barrett's most high-profile meetings will be with Senate Judiciary Committee Chairman Lindsey Graham, R-S.C., Senate Majority Whip John Thune, R-S.D, and a joint sit-down with both Vice President Mike Pence and Senate Majority Leader Mitch McConnell, R-Ky.

Graham, McConnell and Thune have already declared their support for Barrett, as have a number of other Senate Republicans who are familiar with the judge from her 2017 circuit court confirmation.

"She's somebody who respects the Constitution, the law, precedent and is very vigilant in making sure they applied in an evenhanded way," Thune said Monday. "It's going to be very very hard to argue that she isn't qualified for this. In terms of her temperament, her judicial philosophy, she's exactly the kind of justice you would want to see on the Supreme Court.

Barrett will also meet with Sens. 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.

Barrett's meetings will begin at 10:30 a.m. with McConnell and Pence in McConnell's office then continue throughout the day in the Mansfield Room before concluding with Graham at 5:30 p.m.

The meeting with Gardner could be the most important one for Barrett. Gardner is in a tough reelection fight and was initially one of the Republican senators closely watched for whether he would support moving forward with a Supreme Court confirmation less than two months before the presidential election. He eventually said he would back the process. But his statements on the vacancy have not been commitments to a "yea" vote.

"Should a qualified nominee ... be put forward, I will vote to confirm," Gardner said earlier last week.

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He added after Barrett's official nomination: "In the days and weeks ahead, I look forward to meeting with Judge Amy Coney Barrett and thoroughly examining her judicial record as I fulfill my constitutional duty of advice and consent."

Should there be no unexpected defections, Republicans appear to have the numbers to push through the confirmation, which is much closer to the presidential election than any other in modern history. Only Sens. Susan Collins, R-Maine, and Lisa Murkowski, R-Alaska, have said they oppose moving ahead with the confirmation ahead of the election. And Murkowski has softened her stance in recent days, saying she will meet with the nominee as she acknowledged "this process is moving forward with or without me.”

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.

Republicans can afford to lose three total votes and have Vice President Mike Pence break a tie. It's unclear that any other GOP senators, having expressed no qualms about the timing of the nomination, would vote to reject a GOP nominee. But there are still several hurdles in the confirmation process for Barrett to clear, including her Senate meetings, intense media and committee vetting, and committee hearings slated to start Oct. 12, a committee vote, then finally a floor vote on her confirmation -- and that's if things go as planned for Republicans.

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Democrats plan to pressure electorally vulnerable and moderate senators like Gardner, as well as Sens. Mitt Romney, R-Utah, Thom Tillis, R-N.C., Martha McSally, R-Ariz., Joni Ernst, R-Iowa and others.

"By nominating Judge Barrett to the Supreme Court, President Trump has put Americans' health care at grave risk," Schumer said at a Saturday press conference in New York City. "And as COVID-19 continues and we need more health care, the nomination by President Trump of Amy Coney Barrett will mean less health care for over 100 million Americans."

He added: "Health care is the most important issue on the ballot to Americans and as Americans learn Judge Barrett's views on health care and so many other issues, she will become less and less popular, and hopefully they will call their senators and say 'don't vote for someone who will take away my health care.'"

Fox News' Adam Shaw, Marisa Schultz, Chad Pergram and Morgan Phillips contributed to this report.