WASHINGTON — Congress has made significant progress toward passing a renewal of the Zadroga 9/11 Health and Compensation Act, New York lawmakers said Thursday, but they were quick to counsel caution by quoting Yogi Berra: “It ain’t over ‘til it’s over.”

Senate Majority Leader Mitch McConnell (R-Ky.) and House Speaker Paul Ryan (R-Wis.) said they plan to pass the act’s extension by adding it to the $1.1 trillion federal spending omnibus bill, according to Zadroga activist John Feal and Rep. Carolyn Maloney (D-Manhattan).

Democrats and Republicans have agreed on a $3.5 billion extension of the act’s World Trade Center Health Program, and a $4.6 billion renewal of the act’s Victim Compensation Fund for another five years, according the Feal and New York lawmakers.

But McConnell spokesman Michael Brumas said, “The omnibus is still being negotiated so I don’t have a readout on what’s in or out of it.”

The Republican leadership is nearing resolution on how to pay for extending the act, but some other Republican proposals are still under discussion, the lawmakers said.

“We’re getting close. We’ve made good progress in the past few days,” said Sen. Chuck Schumer (D-N.Y.) at a news conference Thursday with Sen. Kirsten Gillibrand (D-N.Y.) and New York City Police Commissioner William Bratton at the Russell Senate Office Building in Washington.

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“The only thing that stands in the way are those who act like they are in no rush to pass this bill, or even the omnibus,” said Schumer, in a reference to McConnell.

Schumer said the Zadroga measure was supposed to be included in the federal transportation bill that passed this week, but on Tuesday McConnell pulled it out.

Feal said McConnell’s chief of staff called him Wednesday evening to say the Zadroga measure would be in the omnibus bill. Ryan told his Republican caucus the same thing Thursday morning, Maloney said.

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“It’s positive news,” said Rep. Peter King (R-Seaford), who said he was being cautious about the Zadroga bill’s prospects. “But until it happens, it hasn’t happened.”

Congress had hoped to pass the omnibus bill by Friday, when the federal government’s money runs out. But lawmakers expect a short-term spending bill to be passed until the omnibus is approved some time in the next week.