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Senate Judiciary Committee chair Chuck Grassley, R-Iowa, said Wednesday that he hoped to have Judge Neil Gorsuch sworn in on the Supreme Court by the middle of April after President Trump said he’d urge Senate Majority Leader Mitch McConnell, R-Ky., to “go nuclear” if his Supreme Court nominee is held up.

Going “nuclear” is Washington code for changing Senate rules to allow a nominee to win confirmation with a slim majority, without first having to get 60 votes. Doing so could have lasting effects on the consideration of future nominees, not just Gorsuch.

"I would guess that we ought to be able to have this on the Senate floor the first week of April if Senator McConnell wants to," Grassley told "Special Report with Bret Baier." "And I think he does want to get it done and then there’ll be the days of debate it takes and then a vote, so that he can be sworn in on the Supreme Court hopefully by the middle of April."

But the threat comes as Democratic lawmakers give conflicting signals over how far they might go to fight Trump’s nominee. Some are urging their colleagues to give the justice a chance and not attempt to block him. But others are demanding Gorsuch hit the 60-vote bar, and laying the groundwork for a potential filibuster, which would require the nominee to garner the support of at least eight Democrats.

On the Senate floor Wednesday afternoon, Minority Leader Chuck Schumer, D-N.Y., voiced “very serious doubts” that Gorsuch is “up to the job,” while noting any one of his colleagues could require the nominee to clear 60 votes.

“There will be 60 votes for confirmation,” he said.

And in a warning to majority Republicans, Schumer said they should not “change the rules” to help Gorsuch. “There’s a special burden on this nominee to be an independent jurist,” he argued, citing concerns not only about the allegedly pro-corporate tilt of the court but also the Trump administration’s respect for the rule of law.

But McConnell called Gorsuch an “outstanding” choice and urged colleagues to give him “fair consideration.” He has not said whether he’d change the rules.

Trump, speaking to reporters, characteristically did not mince words regarding McConnell’s options.

“If we end up with that gridlock I would say if you can, Mitch, go nuclear,” Trump said. “Because that would be an absolute shame if a man of this quality was caught up in the web."

The tensions come as the honeymoon period of Trump’s young presidency appears to be all but over. His immigration executive order last Friday outraged Democrats, who this week tried delaying votes on several Cabinet nominees. This could tee up a dramatic and drawn-out debate over Gorsuch, who won unanimous confirmation from the Senate a decade ago to his current seat on the 10th Circuit Court of Appeals.

Even before Trump named his pick, a contingent of Democrats was inclined to seek payback over Republicans’ refusal to so much as consider then-President Barack Obama’s nominee Merrick Garland last year. And within minutes of the announcement Tuesday night, liberal groups and leaders were taking a hard line.

Sen. Elizabeth Warren, D-Mass., announced her opposition an hour after the ceremony. An arm of the liberal Center for American Progress blasted out a memo saying the Senate should “refuse” to act on any nominee that does not have a “supermajority of upwards of 66 senators.”

The Democratic National Committee was ready with a point-by-point condemnation of Gorsuch, describing him as a “reliable right wing ideologue” who sides with corporations against workers and holds views “more extreme” than the late Justice Antonin Scalia, whose seat he would fill.

But some Democratic figures seem to be looking to lower the temperature on Capitol Hill.

Perhaps the most robust Democratic case for Gorsuch came from Neal Katyal, former acting solicitor general in the Obama administration. In a brief endorsement overnight, he called the federal appeals court judge “one of the most thoughtful and brilliant judges to have served our nation over the last century.”

He also penned a New York Times op-ed praising the nominee’s record – while chastising Trump’s leadership to date.

“I am hard-pressed to think of one thing President Trump has done right in the last 11 days since his inauguration. Until Tuesday, when he nominated an extraordinary judge and man, Neil Gorsuch, to be a justice on the Supreme Court,” he wrote. “There is a very difficult question about whether there should be a vote on President Trump’s nominee at all, given the Republican Senate’s history-breaking record of obstruction on Judge Merrick B. Garland — perhaps the most qualified nominee ever for the high court. But if the Senate is to confirm anyone, Judge Gorsuch, who sits on the United States Court of Appeals for the 10th Circuit in Denver, should be at the top of the list.”

A handful of moderate Democrats went on record urging their colleagues not to filibuster, and at least give the nominee a fair hearing.

“I look forward to meeting with Judge Gorsuch, examining his record, and making a determination of whether to provide my consent,” Sen. Joe Manchin, D-W.Va., said in a statement. “Just as I have all along, I urge my colleagues to put partisan politics aside and allow the vetting process to proceed.”