With the possibility of a government shutdown hanging over Congress’ upcoming holiday break, Senate Democrats now have some leverage on their long-held goal of protecting special counsel Robert Mueller’s investigation. It’s unclear, however, how far they’ll go to use it.

For now, the fight appears mostly focused on President Donald Trump’s demands for funding for a border wall.

Lawmakers face a fiscal deadline on Dec. 7, when they must fund seven appropriations bills, or the government will shut down. The bulk of the disagreement so far has been around funding for a border wall: Trump has told GOP leadership that he wants $5 billion, but Republicans need nine Democrats to meet the 60-vote threshold in the Senate.

That leaves Democrats with some leverage to insist on a provision to protect Mueller, whose investigation some feel is in danger from Acting Attorney General Matt Whitaker, who previously expressed doubt about it as a cable news pundit.

“We need to come together here in the Senate — Democrat and Republican — to pass legislation to protect the special counsel’s investigation,” Senate Minority Leader Chuck Schumer said on the Senate floor Monday. “If the Majority Leader refuses to give it the vote that it deserves, Democrats will push to include it in the must-pass spending bill that we must approve in the next few weeks.”

One bill that would do this — the Special Counsel Independence and Integrity Act — has been lingering in Senate purgatory for months. Introduced by Sen. Chris Coons, Thom Tillis, Lindsey Graham and Corey Booker, it overwhelmingly passed the Judiciary committee in April. But Senate Majority Leader Mitch McConnell has refused to allow it to come to the floor for a vote, arguing that such protection is unnecessary.

But questions about Mueller’s vulnerability were renewed after former Attorney General Jeff Sessions was fired earlier this month and replaced by Whitaker, who will now oversee it. Once McConnell rebuffed Flake’s efforts to force a vote in this context, Flake retaliated by announcing he would refuse to vote for any judicial nominees until he got what he wanted.

Now, it seems that Democrats may follow that lead, but it’s unclear if they are willing to risk a shutdown over it. Trump has mused that it might be a “good time” for a shutdown if he doesn’t get his requested $5 billion for wall funding. If Democrats wanted to, they could draw a similar line in the sand when it comes to incorporating this bill protecting Mueller, but Schumer hasn’t gone that far and neither have his Democratic colleagues.

Sen. Patrick Leahy, the top Democrat on the Appropriations committee, deflected when asked if the provision should even be included in the bill, let alone be used as fodder for a shutdown. “I think it should just be passed,” he said Monday evening. “If you had brought it up this afternoon, it would have passed this afternoon.”

West Virginia Sen. Joe Manchin, who Republicans will almost certainly need to sign on to the final spending bill, had even stronger language. “I’m not supporting a shutdown in any way, shape or form,” he said. “I support Mueller and protecting Mueller. I don’t know why the two [protection and a shutdown] have to be put together.”

There were signs on Tuesday that Republican leadership was rethinking its position and allowing a vote on the floor.

Senate Majority Whip John Cornyn floated the possibility Tuesday morning in an interview with radio talk show host Hugh Hewitt, just hours before Sens. Flake, Coons and Cory Booker announced they would try and force a vote by asking for unanimous consent on the floor. But McConnell quashed that possibility Tuesday afternoon, telling reporters he would “probably” vote to block that move.

“This is a solution in search of a problem,” McConnell said of the bill. “The President is not going to fire Robert Mueller.”

Correction, Nov. 29:

The original version of this story misstated the senator who introduced the Special Counsel Independence and Integrity Act. It was introduced by Sens. Chris Coons, Thom Tillis, Lindsey Graham and Corey Booker, it was not introduced by Sen. Jeff Flake.

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Write to Alana Abramson at Alana.Abramson@time.com.