WASHINGTON - The final version of Democrats' health care overhaul released Thursday contains a fix, its backers said, that would give the cash-strapped state of New York a badly needed shot in the arm: billions of dollars in federal Medicaid money.

The bill also would have a potentially big impact on Long Island, according to Democrats on a key House committee: extending coverage to 161,000 uninsured residents, letting 243,000 young adults stay on their parents' insurance until age 26 and reducing hospitals' cost for treating uninsured people unable pay for their care by $328 million.

Yet despite those sweeteners and selling points in legislation that is on track to be voted on by the House on Sunday, staunch Democratic Reps. Tim Bishop of Southampton and Steve Israel of Huntington, though leaning in favor, refused Thursday to commit to voting yes.

Their reluctance to make the final call until they finish a thorough review underscores the weight and significance of a bill that will cost $940 billion and fundamentally change a sixth of the nation's economy over the next 10 years.

"We're on the verge of making history in a very positive way," said Rep. Gary Ackerman (D-Roslyn Heights).

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"This is not the ideal bill for those of us who wanted it to do more," Ackerman said. "Yet it certainly changes the curve and makes things not just marginally better but much better."

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Ackerman and Rep. Carolyn McCarthy (D-Mineola) both said they'd vote for the bill.

Rep. Pete King (R-Seaford) said he'll vote no on a bill that's "so bad for New York." The GOP argues it gives government too much control over health care and insurance.

The Medical Society of the State of New York said it was disappointed with the bill for failing to permanently restore a 21 percent Medicare payment cut to doctors or to limit medical liability lawsuits.

Insurers said they were concerned that the individual mandate was too weak, allowing too many people to opt out of health care for minimal fines.

Among New York Democrats, the key sticking point and a source of tension has been a provision that gave new federal funds to states to extend Medicaid to people who make between 100 percent and 133 percent of the poverty line.

The old bill sent the money to states that don't cover those people now, but not to New York and other generous states that do cover them.

New York Gov. David A. Paterson said that would cost the state $1 billion a year in lost funding, and he complained the New York delegation had let the state down.

In response, Sen. Charles Schumer (D-N.Y.) said he lobbied President Barack Obama personally to get a boost in Medicaid funds.

The final bill unveiled Thursday included a formula that will give New York a 50 percent boost in federal funds in 2014 and put it on par with all states in 2019, winning praise and thanks from Paterson.

Israel and Bishop, however, said they would wait for the state's final analysis on that funding before making a decision on their Sunday vote.The new bill addressed other concerns of New York lawmakers:

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Cuts to federal payments to hospitals for treating the poor: The bill unveiled yesterday cuts $3 billion less in Medicare payments and $4 billion less in Medicaid payments than the Senate bill.

Medicare Advantage: The new bill more slowly phases out subsidies to private insurers managing Medicare, freezing payments in 2014 and then lowering them after that.