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.) struck a deal Wednesday afternoon to advance the measure, which aides said would put the Senate on course to adjourn sometime later in the day.

The Senate is scheduled to vote to ratify the new Strategic Arms Reduction Treaty on Wednesday afternoon, and is likely to pass the 9/11 bill shortly after that, a GOP aide said.

The Reid-Coburn agreement would cut the cost of the 9/11 bill from $6.2 billion to $4.2 billion, cut the amount that can be paid to attorneys suing for compensation and include new controls to avoid waste, fraud and abuse.

New York Democratic Sens. Charles Schumer and Kirsten Gillibrand hailed the agreement as a “Christmas miracle.”

“Our Republican colleagues have negotiated in good-faith to forge a workable final package that will protect the health of the men and women who selflessly answered our nation’s call in her hour of greatest need … we thank our Republican friends for coming together to fulfill America’s moral obligation to the Heroes of 9/11,” the two said in a statement.

Coburn also said he was happy with the deal: “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,” Coburn said in a statement.

With the 9/11 bill heading toward passage, the Senate should be able to finish work by early evening at the latest, Democratic and Republican aides said.

The House, meanwhile, has been in a holding pattern, awaiting Senate action on the 9/11 measure. 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 Members would be available to clear the 9/11 health care bill if it were to pass the Senate.

Still, nearly one-sixth of House Members did not return for Tuesday’s votes, and Democrats privately conceded there is 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.