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Last Updated Feb 4, 2017 7:32 PM EST

Vice President Mike Pence had a message for Senate Democrats threatening to filibuster President Trumps Supreme Court pick, Judge Neil Gorsuch: Dont do it.

In remarks to the Federalist Society in Philadelphia Saturday, Pence warned that a filibuster of Gorsuch, which would require the Senate to muster a 60-vote threshold to confirm the nominee, would be unwise.

Several [senators] announced their opposition within minutes of his nomination and now theyre even threatening to use the filibuster procedure in the Senate to stop him, Pence told the conservative audience members. Make no mistake about it: This would be an unwise and unprecedented act.

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President Trump wants Senate Republicans to change the rules if needed to confirm his Supreme Court nominee, Judge Neil Gorsuch. Some Senate Demo...

Never before in the history of our country has an associate justice nominee to the Supreme Court faced a successful filibuster, the vice president continued. And Judge Neil M. Gorsuch should not be the first.

The president has also hinted at the possibility of choosing the nuclear option when it comes to Gorsuchs nomination.

In remarks to the press earlier this week, Mr. Trump encouraged Senate Majority Leader Mitch McConnell, R-Kentucky, to go nuclear if theres gridlock in the upper chamber over his nominee. Deploying the nuclear option would change Senate rules allowing Gorsuchs confirmation vote to proceed on a simple majority vote instead of the usual 60 -- a risky precedent to set for political parties in the future.

In his Federalist Society remarks, Pence touted bipartisan cooperation in meeting with Gorsuch, a Denver-based 10th U.S. Circuit Court of Appeals judge who identifies as a constitutional originalist in the mold of the late Antonin Scalia.

In just a few short days, hes already met with 12 senators in both political parties, Pence said. And hes making himself available to meet with all 100 members of the Senate if theyll meet with him.

Pences remarks follow a Saturday morning statement by Senate Minority Leader Chuck Schumer, D-New York, that put Gorsuchs nomination front and center in the ongoing legal battles over Mr. Trumps contentious travel ban.

With each action testing the Constitution, and each personal attack on a judge, President Trump raises the bar even higher for Judge Gorsuchs nomination to serve on the Supreme Court, Schumer said, alluding to Mr. Trumps Twitter smear of a federal judge who handed down a temporary stay of his executive order, which bars refugees and citizens from seven predominantly Muslim nations from entering the U.S. His ability to be an independent check will be front and center throughout the confirmation process.

As demonstrations around the nation continued to protest the ban, Pence highlighted his own familys immigrant past at the Federalist Society, praising the courage of his grandfather for crossing the Atlantic Ocean from Ireland to the U.S.

My grandfather came to this country from a little town in Ireland called Tubbercurry, Pence recounted. He got on a boat, he crossed the Atlantic and he went through Ellis Island. Took a train to Chicago, Illinois, where he drove a bus for 40 years. He was the proudest man I ever knew.

His immigrant grandfather, Pence said, had the right idea about the U.S.

He was right about America, where anybody can be anybody because of the system of liberty that we have enshrined in the Constitution, in the founding documents of this nation, he said.

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Mike Pence warns Democrats against filibuster of Supreme Court pick - CBS News