The Senate must act immediately if it plans on changing and sending back to the House a bill that provides health benefits to Sept. 11 rescue workers, House Majority Leader Steny Hoyer (D-Md.) said Monday night.

Democratic Sens. Charles SchumerCharles SchumerHow Trump can score a big league bipartisan win on infrastructure Overnight Finance: Dems introduce minimum wage bill | Sanders clashes with Trump budget chief | Border tax proposal at death's door GOP senators distance themselves from House ObamaCare repeal bill MORE (N.Y.) and Kirsten GillibrandKirsten GillibrandBill would require sexual assault, social media training for military recruits Dem senator: 'One of our closest allies' expressed concern about intelligence sharing Intel chief quiet on whether Trump asked him to deny Russia evidence MORE (N.Y.) say they have won Republican support for a revised version of the 9/11 health bill, but the House would have to approve any changes to the legislation before the 111th Congress ends in early January.

Hoyer said Democratic leaders do not want to call the House back after Christmas, meaning the clock could run out on the 9/11 legislation. New York lawmakers have pushed the $7.4 billion legislation for years as a way of paying for the treatment of Ground Zero rescue workers who are now suffering from respiratory illnesses linked to the terrorist attacks.

“My plea to Senator Reid is that if you’re going to send us anything that we need to deal with, send it, frankly, by [Tuesday],” Hoyer told The Hill. “I don’t think that’s possible, but my members want to get home for Christmas, and I think bringing them back between Christmas and New Years — hopefully, I’d like to avoid that.”

The majority leader, however, did not explicitly rule out the House returning to act on the 9/11 bill. “I suppose anything is possible,” he said.

Aides to Senate Majority Leader Harry ReidHarry ReidGOP frustrated by slow pace of Trump staffing This week: Congress awaits Comey testimony Will Republicans grow a spine and restore democracy? MORE (D-Nev.) said the Senate would vote Tuesday on a stopgap government funding bill and on the New START treaty, but likely not the 9/11 bill. And if Republicans do not agree to waive procedural rules to expedite the legislation, the earliest a final vote could be held would be Thursday, just two days before Christmas.

Mindful of the time crunch, Schumer begged the GOP not to filibuster the bill if it comes up again. “Please don’t delay this bill. Let it come to a vote, and we will win,” Schumer said Monday on ABC’s “Good Morning America.”

He said he spoke with House Speaker Nancy Pelosi (D-Calif.) about the legislation, but the Speaker’s office has made no commitments to stay in session to vote on a new Senate bill.

Gillibrand said she hopes the Senate will get to the 9/11 healthcare bill on Tuesday.

“The hope is we get the START treaty completed tomorrow and we can vote tomorrow,” Gillibrand told The Hill.

The Senate voted to advance the 9/11 bill on Dec. 9, but Republicans blocked it with a filibuster.

Reid can bring the bill back to the floor at any time with a motion to reconsider. It would have to win 60 votes to overcome a filibuster and receive a vote on final passage. 

The bill could pass the Senate by Tuesday evening only if GOP opponents of the New START treaty and the 9/11 healthcare program agree to waive procedural rules that require as many as 30 hours to elapse between votes.

—Alexander Bolton contributed to this article.