DEAL STRUCK ON 9/11 HEALTH BILL, SENATE PASSAGE VERY LIKELY…. Key players in the Senate debated privately for hours last night, trying to work out a deal on the 9/11 health bill. As of this morning, the fate of the Zadroga 9/11 Health and Compensation Act, which would pay health care costs for 9/11 rescue workers, sickened after exposure to toxic smoke and debris, was still in doubt.

The votes appeared to be in place to overcome a Republican filibuster, but in the interests of time, the Senate was seeking unanimous consent. Sen. Tom Coburn (R-Okla.) refused to go along.

As of this afternoon, the New York Daily News, which has done fantastic work covering the issue, reports that a deal appears to have been struck that will allow for final passage.

Sens. Chuck Schumer and Kirsten Gillibrand met with other senators’ staffers and aides to Rep. Carolyn Maloney’s office until well after midnight to cut a new deal on a measure to aid ailing 9/11 responders.

The agreement trims the cost of the package to $4.3 billion, sources close to the deal said.

The proposal had initially cost $7.4 billion, and had been trimmed earlier this week to $6.2 billion.

Senators reached a final agreement on the proposal at about 11:30 Wednesday morning after the New York Democrats met for an hour with the prime GOP opponents, Sens. Mike Enzi of Wyoming and Tom Coburn of Oklahoma.

The Senate leadership has reportedly signed off on the agreement, and expects to pass the bill this afternoon. Greg Sargent and ABC’s Rick Klein are hearing the same thing.

If all goes according to plan — and at this point, it should — this should clear quite a few things up. Not only will 9/11 heroes be able to get much-needed medical care, but New START ratification can proceed this afternoon, too. The House, which has been cooling its heels waiting for the Zadroga bill, should be able to pass this with relative ease — more than 90% of House Republicans opposed it when it initially passed the chamber, but given recent developments, and unanimous Senate support, it stands to reason they’ll be more supportive later today.

As for the substantive changes, there’s a real concern that reducing the cost of the package to $4.3 billion, from $7.4 billion, will undercut the amount of care available, and the number of rescue workers who’ll be eligible. It’s possible, then, that the next Congress will have to revisit this issue in the future.

In the meantime, Democratic negotiators very likely concluded that $4.3 billion is far better than zero. For those sick first responders and their families, this is still excellent news.

Update: At 2:31 p.m., the Senate unanimously approved the 9/11 health bill. The House is expected to act within two hours.

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Follow Steve on Twitter @stevebenen. Steve Benen is a producer at MSNBC's The Rachel Maddow Show. He was the principal contributor to the Washington Monthly's Political Animal blog from August 2008 until January 2012.