ATLANTA — Georgia Republican lawmakers could face the wrath of a GOP powerbroker who is warning them not to renew a hospital tax that supports care for poor patients.

If they agree to end the tax, it would worsen the strain on an already stretched state budget and could burden hospitals and their emergency rooms with patients who lack insurance or don’t have enough coverage to pay for their care.

Anti-tax advocate Grover Norquist, president of Americans For Tax Reform, recently told the Republican-dominated General Assembly in a letter that renewing the Hospital Provider Payment Program would violate the anti-tax pledges of about four dozen lawmakers.

Lawmakers adopted the tax in 2010 as state tax collections tanked because of the Great Recession. It uses tax money paid by the hospitals to generate an even larger pot of state and federal health care money that then flows back to the hospitals.

Hospitals with a large share of poor patients get more back in increased Medicaid payments — a government insurance program that covers the poor — than they pay in hospital taxes. Hospitals with a larger share of patients covered by Medicare or private insurance get fewer benefits than they pay out in taxes. Still, those hospitals get an indirect benefit. They don’t have to directly bear the costs of caring for the poor because the tax helps stabilize the budgets of hospitals serving poorer populations.

Norquist said Georgia lawmakers should let the tax expire on July 1 because he believes it thwarts job growth and encourages more federal spending. Although the lawmakers who signed the anti-tax pledge lack enough votes to prevail on their own, their ranks are large enough to force a debate.

“Make good on the promise you made when the bed tax was instituted as temporary — let it expire ... and continue your hard work to make Georgia an economically competitive destination for jobs, investment and growth,” Norquist wrote.

Republican Gov. Nathan Deal, who signed Norquist’s pledge, must decide whether to recommend renewing the tax as part of his next budget proposal due in January. Deal spokesman Brian Robinson declined to say what Deal would do.

The tax generates significant money. Hospitals are expected to pay almost $234 million in taxes during the one-year period that started in July, according to an August estimate by Georgia’s Department of Community Health. That spending will prompt the U.S. government to contribute an additional $448 million into Georgia’s health care coffers. Georgia pays a large portion of it back to hospitals in the form of increased payments for Medicaid services.

Executives from several health care entities that serve a broad swath of Medicaid beneficiaries followed Norquist’s warning with a letter of their own to lawmakers.

Co-signers from Grady Health System, Children’s Healthcare of Atlanta, HomeTown Health and Memorial University Medical Center warned that scrapping the tax could result in steep cuts in the payments to health care providers, with some of them, in turn, limiting their services for Medicaid patients. The group noted that 46 other states and Washington, D.C., impose similar bed taxes to generate more federal Medicaid financing.

“If we left the federal match on the table as recommended by Mr. Norquist, the burden of funding Medicaid and caring for the most vulnerable Georgians would fall entirely on the backs of state and local taxpayers,” the executives wrote. “This does not make sense when federal funds are made up of tax dollars that Georgia residents and business pay to the federal government.”

Some Republicans oppose eliminating the tax. Rep. Terry England, R-Auburn, chairman of the House Appropriations Committee, said the Medicaid program is already facing a $300 million deficit because more people have qualified for government benefits after losing their jobs. He was skeptical that Georgia could absorb the additional loss.

“Folks, I think, see and understand the need to possibly renew it because of the way it helps the critical care hospitals, especially the hospitals in the rural areas,” England said.

Republican Rep. Jason Spencer, R-Woodbine, who signed Norquist’s pledge and works as a physician’s assistant in southeastern Georgia, said money lost by hospitals could have been used for other purposes, such as hiring nurses to eliminate wait times.

“What’s really happening is that they’re subsidizing these other hospitals that always operate in the negative,” Spencer said. “My hospital is subsidizing care in a community far, far away in Atlanta.”

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