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(CNN) —  

Retiring Republican Sen. Jeff Flake said Wednesday that he will not vote to confirm the Trump administration’s judicial nominees on the Senate floor or advance them in the Senate Judiciary Committee if legislation to protect special counsel Robert Mueller does not receive a Senate floor vote.

Flake made the new judicial threat after he and Sen. Chris Coons, a Delaware Democrat, unsuccessfully attempted to force a Senate vote on the special counsel legislation Wednesday. Senate Majority Leader Mitch McConnell objected to the request for a vote from Flake.

But the Arizona Republican’s threats on judicial nominees could complicate matters in the Judiciary Committee, where Republicans have an 11-10 majority. There are currently 21 judicial nominees pending in the committee and 32 who are awaiting a floor vote, Flake said.

“We have been told that the bill that Sen. Coons and I will move to bring up shortly is not necessary, as there have been no indications that the independence of Mr. Mueller’s investigation is in jeopardy,” Flake said. “That may have been an arguable position before last week. But it is not arguable anymore.”

Flake and a handful of other Republican senators, such as Susan Collins of Maine, have said they think the legislation to protect the special counsel is necessary after President Donald Trump fired his attorney general, Jeff Sessions, and replaced him with acting Attorney General Matt Whitaker, who has been openly critical of the Mueller probe.

“The President now has this investigation in his sights, and we all know it,” Flake said.

In a news conference following his floor speech, Flake said he agreed with Democrats that Whitaker should recuse himself from the Mueller investigation. He noted that he had used the same leverage over judges to force a Senate vote on tariffs and he was prepared to carry out his threat through the end of the year if necessary.

“The President has said that he’s not going to move on the special counsel. But that’s not enough,” Flake said. “And perhaps that’s what gives comfort to the majority leader. … But it doesn’t give comfort to me.”

The committee will hold a business meeting on Thursday with 14 district court and circuit court judges on the agenda, but they will be held over for votes for at least a week under the committee’s normal procedures.

The special counsel bill passed the Senate Judiciary Committee in April as a bipartisan compromise hammered out by two Republicans and two Democrats, including Coons, backed by Senate Judiciary Chairman Chuck Grassley, an Iowa Republican.

McConnell and other Senate Republicans say the legislation is not necessary because the President is not about to fire Mueller or undermine the investigation, and Senate Republican leaders have made no effort to put it on the Senate floor.

One of the bill’s Republican co-authors, Sen. Thom Tillis of North Carolina, said he supports the policy but doesn’t see an immediate need to pass the measure.

“I don’t think the President has any intention of removing Mueller. I’m all about getting this on the books so no future President can make that kind of a bad decision,” Tillis said Wednesday. “I’ve had discussion with the President. Everyone said it was hours away back in August. Didn’t happen. So I think it’s another false crisis. But it’s important legislation ultimately to get passed.”

Tillis said that Sessions’ firing didn’t increase the urgency for the legislation.

“I don’t think it’s increased the threat of Mueller being prevented from finishing his business. And I think most of this is going to be a non-event over the next month-and-a-half as the investigation winds down,” he said.

Flake and Democrats disagree, and they aren’t dropping the matter even if they can’t force a floor vote on Wednesday.

Senate Minority Leader Chuck Schumer suggested Tuesday that Democrats may try to tack on the special counsel legislation to the spending bill that Congress must pass during the lame-duck session to prevent a government shutdown.

“If Mr. Whitaker does not recuse himself, we Democrats are going to attempt to add legislation to the must-pass spending bill in the lame duck session that will prevent acting Attorney General Whitaker from interfering with the Mueller investigation in any way,” Schumer said.

CNN’s Manu Raju, Ted Barrett and Jake Tapper contributed to this report.