Updated: 1:39 p.m.

The 111th Congress was heading toward the finish Wednesday as the Senate reached a deal on a 9/11 health care bill, the last piece of unresolved business.

Senate Majority Leader Harry Reid (D-Nev.) and Sen. Tom Coburn (R-Okla.) have negotiated an agreement to advance the measure, which aides said could put the Senate on course to adjourn sometime Wednesday evening.

“I’m pleased the sponsors of this bill agreed to lower costs dramatically, offset the bill, sunset key provisions and take steps to prevent fraud. Every American recognizes the heroism of the 9/11 first responders, but it is not compassionate to help one group while robbing future generations of opportunity. I’m pleased this agreement strikes a fair balance and improves the bill the majority attempted to rush through at the last minute,” Coburn said in a statement.

The Senate is scheduled to vote to ratify the new Strategic Arms Reduction Treaty on Wednesday afternoon.

The House, meanwhile, has been in a holding pattern as the Senate tries to unlock the 9/11 bill. The chamber convened Wednesday morning and cleared the annual defense authorization bill before recessing subject to the call of the chair.

Democratic leaders have acknowledged the difficulty of keeping Members — particularly those who are retiring or lost their seats on Nov. 2 — in Washington for votes as Christmas approaches. But they have kept the chamber in session so that Members would be available to clear the 9/11 health care bill once and if it passes the Senate.

Still, nearly one-sixth of House members did not return for Tuesday’s votes, and Democrats privately concede that there’s little they can do to entice their colleagues to stick around. Between 75 and 100 lawmakers were absent for each of the seven votes held Tuesday, including a number of recently defeated Democratic lawmakers.

House Republican leadership aides said they have not made any effort to keep their Conference in Washington this week, citing their long opposition to the lame-duck session.

Jackie Kucinich contributed to this report.