(Bloomberg) -- Conservative groups are pressing Republican leaders in Congress to renew a restriction on the U.S. government’s ability to reimburse health insurers for some losses under the Patient Protection and Affordable Care Act, also known as Obamacare.

Organizations including Heritage Action for America, the Club for Growth, and Americans for Tax Reform want the limits added to a broad spending bill that Congress must pass by Dec. 11 to avoid a government shutdown.

They made their appeal Tuesday in a letter to House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell.

The groups are targeting a program, called "risk corridors," intended to partially reimburse insurers who lose money on plans sold under the 2010 Affordable Care Act.

The letter comes a week after the U.S. Centers for Medicare and Medicaid Services said it would ask Congress to cover shortfalls in the program.

“Taxpayers should not be on the hook for any more of Obamacare’s failures, and so we urge you to ensure that their voices prevail by continuing to include language preventing risk corridors from becoming a taxpayer bailout in any future appropriations bill,” the groups wrote.

A spokesman for McConnell, a Kentucky Republican, did not immediately respond to a request for comment. A Ryan spokeswoman, AshLee Strong, declined to comment and referred questions to the House Appropriations Committee.

Spokespeople for Democrats and Republicans on the committee both declined to comment.

Insurers asked for $2.87 billion from the risk corridors program for losses in 2014, the first year of coverage using PPACA's insurance exchanges.

On Oct. 1, the Department of Health and Human Services said it could only pay $362 million, less than 13 cents on the dollar, because of restrictions already imposed by Congress.

"Consumers and health plans have faced a number of challenges in the transition to the new exchange market," Clare Krusing, a spokeswoman for America’s Health Insurance Plans, the industry’s Washington lobby group, said in an e-mail. "The focus should be on providing stability for individuals and families and avoiding coverage disruptions in the future."

The program was intended to help keep insurance premiums stable in the first three years of PPACA, and it expires at the end of the 2016 fiscal year next September.

The conservative groups asking for risk corridors to be curtailed said in their letter that they had predicted insurers would likely demand "much more in returns from the program than they were putting into it."

“That prediction has turned out to be true,” the groups said. The letter was signed by Heritage Action for America Chief Executive Officer Michael Needham, Americans for Tax Reform President Grover Norquist, Club for Growth President David McIntosh, and representatives of more than a dozen other groups.

Money to make risk corridor payments is collected from insurers that turn a profit selling plans in the government-run marketplaces created by PPACA.

The government office that administers the program, the Center for Consumer Information and Insurance Oversight, said in a Nov. 19 memo to insurers that it would use risk corridor collections in 2015 "and if necessary, 2016" to pay the balance it owes for 2014.

In the event of a shortfall in 2016, the government "will explore other sources of funding for risk corridors payments, subject to the availability of appropriations," the memo said. "This includes working with Congress on the necessary funding."

Representative Jim Jordan, an Ohio Republican who chairs the hard-right Freedom Caucus, suggested that the government would find little sympathy.

"Obamacare’s risk corridors program will cost American taxpayers billions if Congress does not continue to restrict its use," Jordan said in a statement e-mailed by a spokesman.

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