Judge Neil Gorsuch cleared his first test vote Monday in his quest for the Supreme Court, gaining approval of the Senate Judiciary Committee in a party-line vote that presages a nasty, history-making fight on the chamber floor this week.

Democrats say they have enough votes to successfully mount the first-ever partisan filibuster of a Supreme Court pick, and Republican leaders say that if Democrats follow through on that threat, Republicans will be forced to use the “nuclear option” to change the rules.

“It’s not too late for our Democratic colleagues to make the right choice,” Senate Majority Leader Mitch McConnell pleaded with Democrats. He said the fight Democrats have picked is the wrong fight, choosing to force a showdown over a nominee that all sides agree has the highest legal credentials.

Judge Gorsuch cleared the Senate committee in an 11-9 vote, with every Republican backing him and every Democrat on the panel opposing him.

Mr. McConnell has set a final vote on Judge Gorsuch’s confirmation for Friday, with the nuclear option showdown coming a day earlier.

His Democratic opponents said the judge has skirted the big issues, leaving them guessing as to how he would rule.

“Judge Gorsuch’s views were difficult to discern because he refused to answer many questions — even basic questions that had been answered by previous nominees,” said Sen. Dianne Feinstein, the top Democrat on the Judiciary Committee.

Democrats have offered a long list of reasons — sometimes conflicting ones — for why they will not back Judge Gorsuch.

A handful of senators have said they can’t stomach anyone nominated by Mr. Trump at a time when the president’s team is facing an investigation into its dealings with Russia.

Some Democrats wanted Judge Gorsuch to commit to overturning one precedent on First Amendment protections of campaign speech, while also demanding he pledge fealty to other precedents on abortion rights.

Senate Minority Leader Charles E. Schumer, meanwhile, said Democrats are still seething over the way Republicans treated President Obama’s pick for the same seat, Judge Merrick Garland, whom Republicans refused to even grant a hearing, much less a vote.

Mr. Schumer said his decision to launch the first-ever partisan filibuster of a Supreme Court nomination was a fair retaliation.

“The fact of the matter is, Republicans blocked Merrick Garland using the most unprecedented maneuvers. Now we are likely to block Judge Gorsuch, and that means that neither party has gotten their party’s choice in the last two years,” the New York Democrat said.

Mr. Schumer says he wants Mr. Trump to pull Judge Gorsuch’s nomination and instead find a new pick Democrats will agree to.

On Monday more Democrats announced that they will stand with Mr. Schumer, who now appears to have at least 41 votes to support the filibuster.

Sen. Christopher A. Coons, a Delaware Democrat who had delayed taking a stance, tried to cast his support for the filibuster as a marker for the next Supreme Court fight, saying he’s opposing Judge Gorsuch in order to force President Trump to the negotiating table next time.

Mrs. Feinstein and Sen. Patrick J. Leahy, two senior Democrats who’d also waited to announce their decisions, both made clear they will vote against Judge Gorsuch.

That leaves just four Democrats who have said they will join all 52 Republicans in support. Sixty votes are needed to overcome a filibuster.

Should Democrats succeed in their filibuster, Mr. McConnell would be forced to use the “nuclear option,” taking advantage of a controversial shortcut to change Senate rules and reduce the threshold for overcoming a filibuster from 60 votes to just a simply majority.

Democrats went nuclear under Senate Majority Leader Harry Reid in 2013 for Mr. Obama’s lower-court nominees, but left the filibuster’s 60-vote threshold in place for Supreme Court debates.

Sen. Lindsey Graham, South Carolina Republican, blasted Democrats for hypocrisy, saying if roles were reversed, they would have done the same thing the GOP did last year in blocking Judge Garland. And Mr. Graham said Democrats would also be preparing to pull the nuclear trigger now — indeed, Mr. Reid said so late last year.

Mr. Graham, who voted for both of Mr. Obama’s Supreme Court nominees, Justice Elena Kagan and Justice Sonia Sotomayor, said Democrats’ gripes sounded like “the arsonist complaining about the fire.”

“I find it ironic and sad that we’re going to change the rules over somebody that’s lived such a good life — that’s been such a good judge for such a long time,” said Mr. Graham. “There’s nothing wrong with him. There’s a lot wrong with modern politics and the Senate.”

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