WASHINGTON (AP/CBSNewYork) — Backers of a 9/11 bill in Congress that would help people who became sick after working in the World Trade Center dust created by the Sept. 11 attacks say they are optimistic the Senate will approve the measure before the lame-duck session ends.

New York Democratic Sens. Kirsten Gillibrand and Chuck Schumer said Sunday they are offering a less-costly alternative to the original bill to aid 9/11 responders and survivors, saying that they believe it will gain needed support from the GOP.

Schumer said the new version of the James Zadroga bill has been scaled back from $7.4 billion to $6.2 billion.

At a news conference Sunday, Gillibrand proclaimed “we are on the verge of a Christmas miracle.”

“Barring a setback, we believe we are on the path to victory by the end of the week,” Schumer said Sunday.

Republicans have raised concerns about the bill’s cost and how to pay for it.

Gillibrand tried to diffuse those concerns and said that after working with Republican colleagues, supporters have come up with a “new way to pay for the bill.”

Gillibrand said that a federal government fee would be imposed on contracts with foreign countries that have not signed a certain procurement agreement with the United States. In addition, an existing fee on H1B and L1 visas would be extended.

Schumer said lawmakers concerned with Amercan jobs staying the country “should support this proposal.”

“This bill reduces the deficit,” Schumer said, “CBO (Congressional Budget Office) estimates that we raise $57 million more than the bill costs.”

Reps. Carolyn Maloney, Jerrold Nadler and Peter King released a joint statement Sunday calling the changes to the bill “a big step forward.”

1010 WINS’ Kyle McMorrow talks to Rep. Peter King

“What 9/11 rescuers and survivors really want for the holidays is to pass the Zadroga Act – and we’re on the doorstep of doing just that,” the statement said.

King told 1010 WINS that it was “essential that it get done before Christmas” because if it didn’t, the process would have to “start all over again” with a new Congress.

“America will be watching very closely to how this Senate votes on something that goes to the fundamental issue of who we are as Americans and whether we stand by our heroes,” Gillbrand said.

Supporters were three votes short of the 60 votes they needed for the bill on a recent test vote.

The House has passed the original bill but would have to consider any new version.

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