WASHINGTON -- After a filibuster and threats of obstruction by Sen. Tom Coburn (R-Okla.), the Senate unanimously passed a bill on Wednesday that would provide health care for first responders to the 9/11 terrorist attack. Sens. Kirsten Gillibrand and Chuck Schumer reached a deal with Republican senators to support the bill earlier in the afternoon. (UPDATE: The House has also passed the legislation.)

Gillibrand and Schumer, the bill's chief sponsors, lobbied hard for the legislation to be introduced again in the lame-duck session, when they could still ensure House support. But on Tuesday, they hit a snag when Coburn vowed to block the bill, saying he wanted it to be funded through spending cuts.

Coburn also claimed the bill had been fast-tracked and skipped committee. But in fact the Senate Committee on Health, Education, Labor and Pensions held a hearing on the bill in June -- Coburn, a committee member, missed it.

Sen. Mike Enzi (R-Wyo.) also said he would oppose the bill so the Senate could hold hearings on it in the future.

But just before leaving town for Christmas, senators reached a deal to ensure Republican support for the bill. It will now go for a vote by unanimous consent. The House remained in Washington to act on the bill.

The new deal reduces the cost of the bill by $6.2 billion from its previous Senate version and $7.5 billion from the version that passed the House, according to a statement from Coburn's office. It calls for closing the Victims Compensation Fund in 2016 instead of 2031, preventing claimants from pursuing civil lawsuits if rejected from the fund, and limiting infrastructure costs and attorney fees.

"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 after the deal was reached. "I'm pleased this agreement strikes a fair balance and improves the bill the majority attempted to rush through at the last minute."

If the bill passes, it will be another success for Democrats during a busy lame-duck session.

"This has been a long process, but we are now on the cusp of the victory these heroes deserve," Gillibrand and Schumer said in a joint statement.