Senate Majority Leader Mitch McConnell said a new bill that would shield special counsel Robert Mueller from being fired by President Donald Trump will not be brought up on the Senate floor, ending a bipartisan effort that had been in the works for months.

“I'm the one who decides what we take to the floor. That's my responsibility as the Majority Leader, and we will not be having this on the floor of the U.S. Senate,” McConnell, R-Ky., said emphatically in an interview Tuesday on Fox News.

The comments are the first time the Republican leader has said he will not bring the bipartisan legislation up for consideration, despite renewed concern – mostly from Democrats, although a handful of Republicans have joined in – that the president will fire Mueller or Deputy Attorney General Rod Rosenstein, who oversees the investigation of possible collusion between the Trump campaign and the Russians.

The president has recently stepped up his public and private criticism of DOJ officials and the Russia probe, lashing out at Mueller on Twitter and openly musing to reporters about firing the special counsel in a meeting last week, saying “many people” are telling him to sack Mueller, adding, “We’ll see what happens.”

Despite that, McConnell has said he does not believe the president will fire Mueller.

Senate Democratic Leader Chuck Schumer said it would be “a mistake” not to pass the bill, adding, “We ought to head off a constitutional crisis at the pass, rather than waiting until it’s too late.”

Nevertheless, McConnell's sentiment is echoed by many of his fellow Senate Republicans.

Sen. Jim Lankford, R-Okla., told reporters Tuesday that he did not see a need for the legislation, calling it “a political distraction.”

“It would not hurt if we passed legislation to send a message to the White House that we want the investigation to continue,” Sen. Collins, R-Maine, told ABC This Week anchor George Stephanopoulos on Sunday. “But the fact is that the president is never going to sign that legislation, and there are some legitimate constitutional concerns about it.”

But Senate Judiciary Committee Chairman Chuck Grassley, who last week said Trump would be committing “suicide” if he sacked the special counsel, scheduled the Mueller protection bill for consideration in his committee in just over a week.

The measure would give any special counsel 10 days to seek an expedited judicial review if he or she were fired. Sen. Thom Tillis, R-N.C., Lindsey Graham, R-S.C., Chris Coons, D-Del., and Cory Booker, D-N.J., introduced the bill.

“I don’t know from where Leader McConnell gets his confidence that President Trump will not take action to end this investigation, given the number of times this President has tweeted or has spoken directly or indirectly in ways that I think threaten this investigation,” Coons said. “The reality here is that there are stronger and stronger signals that this President -who has acted in an abrupt and unconventional and untraditional and unwise way - may very well do exactly the same against Bob Mueller and it would be wise for us to take it up and consider it.”

Grassley, an Iowa Republican, who, like a number of Republicans, has expressed concern that the bill is an unconstitutional infringement on the president’s powers as chief executive, had been preparing an amendment to the legislation, though the contents of the measure have not yet been released. Sen. Dianne Feinstein, D-Calif., said she expected to receive a copy of that amendment on Wednesday.

A Grassley aide told ABC News that the McConnell announcement would not change committee plans.

“This doesn't really change anything as far as the committee is concerned. Chairman Grassley said if the authors of the various proposals put forward a consensus bill, he'd bring it up. That remains the plan,” the aide said in an e-mailed statement to ABC News.

That is not likely to be welcome news to a number of Republicans who have also voiced private concerns about bucking a president still popular with the GOP base.

House Democrats have introduced a companion bill.

House Speaker Paul Ryan has not committed to giving that measure a floor vote.