Majority Leader Steny Hoyer announced Tuesday morning that the House could adjourn for the year late Tuesday or early Wednesday.

But the Maryland Democrat acknowledged that the schedule hinges on the Senate.

Hoyer predicted the House would vote “within a few hours” on a continuing resolution to fund the government through March 4, “assuming the Senate moves forward on that.” The Senate voted to invoke cloture, or cut off debate, on the measure Tuesday morning. Senators are expected to approve the CR later Tuesday.

House Democratic leaders also want to complete action on a bill to provide health benefits for 9/11 workers. Like the CR, that measure is pending in the Senate. Hoyer said he had spoken to the bill’s proponents in the Senate, most recently Sen. Kirsten Gillibrand (D-N.Y.), to determine whether Senators would be able to send the measure back to the House, “hopefully by tonight or early tomorrow morning.”

“Obviously the closer we get to Christmas, the less likelihood there is of Members being willing to stay and finish business that may or may not come from the Senate,” Hoyer said. “But we are pursuing that. … We want to pass it. We think it’s an important piece of legislation.”

But Hoyer was noncommittal about how long he might keep the House in session to try to get the measure finished.

In the meantime, the House on Tuesday was working to clear a number of other last-minute items, including a food safety bill and the America COMPETES Act.