Senate Majority Leader Mitch McConnell, R-Ky., joined from left by Sen. John Thune, R-S.D., and Majority Whip John Cornyn, R-Texas, speaks to reporters following a closed-door strategy session on Capitol Hill in Washington, Tuesday, April 17, 2018. (AP Photo/J. Scott Applewhite)

Senate Majority Leader Mitch McConnell, R-Ky., joined from left by Sen. John Thune, R-S.D., and Majority Whip John Cornyn, R-Texas, speaks to reporters following a closed-door strategy session on Capitol Hill in Washington, Tuesday, April 17, 2018. (AP Photo/J. Scott Applewhite)

WASHINGTON (AP) — Senate Majority Leader Mitch McConnell on Tuesday thwarted a bipartisan effort to protect special counsel Robert Mueller’s job, saying he will not hold a floor vote on the legislation even if it is approved next week in the Senate Judiciary Committee.

McConnell said the bill is unnecessary because President Donald Trump will not fire Mueller.

“We’ll not be having this on the floor of the Senate,” McConnell said on Fox News.

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His comments came amid widespread opposition to the bill among members of his caucus, with several GOP senators saying the bill is unconstitutional. Others said it’s simply not good politics to try and tell Trump what to do, likening the legislation to “poking the bear.”

The bipartisan legislation was introduced last week as Trump publicly criticized Mueller, who is investigating potential ties between Russia and Trump’s 2016 campaign as well as possible obstruction of justice by the president. Trump, fuming about a raid of his personal lawyer’s office by a different division of the FBI, said last week that the Mueller investigation is “an attack on our country” and is “corrupt.”

Trump has also privately pondered firing Deputy Attorney General Rod Rosenstein, who is overseeing Mueller’s investigation.

Within a day of Trump’s criticism, Republicans Thom Tillis of North Carolina and Lindsey Graham of South Carolina combined two bills they introduced last summer to protect special counsels. They introduced the new bill along with Democratic Sens. Chris Coons of Delaware and Cory Booker of New Jersey, and Senate Judiciary Chairman Chuck Grassley, a Republican, announced that his committee would vote on the bill.

The legislation would give any special counsel a 10-day window to seek expedited judicial review of a firing, and would put into law existing Justice Department regulations that require a firing to be for “good cause.”

Democrats immediately jumped on the legislation, but many Republicans have been cool to it.

At least three of the 11 GOP members of the Judiciary panel have said they will vote against it and another five have said they have questions about its constitutionality. Grassley is one of those with concerns, but said he felt obligated to hold a vote.

Republicans off the committee had questions too — and some acknowledged that it could be politically difficult.

South Dakota Sen. Mike Rounds said Tuesday that Trump should make the decision on his own and be responsible for the consequences.

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“I think having Congress tell him what we believe he should do in this case is simply poking the bear, and I’d just prefer not to do that,” Rounds said.

Oklahoma Sen. Jim Lankford said the bill is a “political distraction.”

“You create this whole constitutional political stir over something that is not going to happen,” he said.

Others said there was little point.

“It’s about as popular as cholera with the leader in the Senate and it’s about as popular as malaria in the House,” said Louisiana Sen. John Kennedy, a member of the Judiciary panel. “I think most people think we’re picking an unnecessary fight with the president.”

Coons bristled at the criticism that the legislation is unconstitutional, noting that several courts have upheld similar special counsel statutes.

“If I were convinced this were unconstitutional, I would not be moving it,” said Coons, a lawyer.

At a September hearing on the two separate bills, before they were combined, scholars were divided on whether the bills were constitutional, with some voicing concerns that allowing the judicial branch that authority over an executive decision may not pass muster in the courts.

“I think it’s probably unconstitutional and I don’t think there’s any realistic chance that the president will fire Mr. Mueller,” Sen. John Cornyn, the No. 2 Republican in the Senate and the former Texas attorney general, said Tuesday.

McConnell agreed, adding that Trump would never support the legislation.

“Just as a practical matter, even if we pass it, why would he sign it?” McConnell said in the Fox interview.

Republicans who have talked to the White House almost uniformly have held the line that Trump will not fire Mueller or Rosenstein — including Tillis and Graham, who say they are pushing the legislation because it would be good policy under any president.

“I don’t think he’s going to fire Mueller, but I think institutionally it would be nice to have some protections,” Graham said Tuesday.

Tillis acknowledged last week that he had taken some “heat” from conservatives for the bill, but told the Judiciary panel, “this is really an opportunity to take an ethical stand, and not do it when the situation benefits you.”

Democrats said Republicans opposed to the legislation were simply protecting Trump.

Connecticut Sen. Richard Blumenthal, a member of the Judiciary Committee, said the argument over constitutionality is a “red herring used by some of my colleagues as a pretext for opposing the bill, when they really have other reasons.” He gave no specifics.

Virginia Sen. Mark Warner, the top Democrat on the Senate intelligence committee, said the special counsel bill is “so much more” than another policy debate.

“I think this will be one that history will judge us all,” Warner said.

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Associated Press writer Lisa Mascaro contributed to this report.