Mayor Vincent C. Gray is heading for a final showdown Tuesday with D.C. Council member David A. Catania over city funding for a health insurance program that pays for hospital care for thousands of undocumented immigrants.

When he unveiled his fiscal 2013 budget this spring, Gray (D) proposed a $20 million cut to the D.C. Healthcare Alliance, which insures an estimated 19,000 residents, the vast majority of whom are undocumented immigrants.

But Catania (I-At Large), the chairman of council’s Health Committee, is fighting to restore the money. When he marked up the Health Committee budget this month, Catania found $20 million in savings from Medicaid and other health programs to restore the funding.

Catania has argued that Gray’s proposal would burden hospitals, which would be forced to provide uncompensated care to the uninsured. Catania also views the alliance program as a key linchpin to city efforts to ensure all residents are insured.

But Gray worries Catania’s plan will undermine other parts of the Health Department budget. Instead, Gray has proposed a new formula that would make it easier for hospitals to dip into locally funded accounts they maintain to receive payment when they treat an uninsured patient.

The two men spent the past 10 days trying to reach a compromise, but the talks broke down.

In a statement to council members and the media Monday afternoon, Gray said he had the “stronger, more responsible approach.”

“The Administration’s approach maximizes federal revenue, saves more than $5 million of funds, responsibly shares costs with hospitals, while maintaining important benefits for the District’s most vulnerable residents,” Gray said.

But Brendan Williams-Kief, a Catania spokesman, said Gray’s plan still does not guarantee that uninsured patients will receive the hospital care they need.

“He put it together less than a week before a vote, the hospitals haven’t signed off on it, and the whole plan relies on the hospitals signing on,” Williams-Kief said. “We are maintaining the benefit. That is our intention.”

On Tuesday, the council will consider both plans when it takes up the budget. According to insiders in the John A. Wilson Building, Catania’s plan appears to have more support than Gray’s.

But more than a dozen nonprofit organizations, including Whitman-Walker Clinic and Planned Parenthood of Metropolitan Washington, sent a letter to Gray on Tuesday expressing opposition to Catania’s proposal. They worry that Catania’s plan would result in cuts to other health programs.

“We have stressed that full restoration of the Alliance hospitalization benefit is one of our highest priorities . . . however, doing so must not come at the expense of any other essential health and human services program,” states the letter, also signed by the D.C. Primary Care Association and the Legal Aid Society of the District of Columbia. “Your proposal shifts some costs to the Federal government for Emergency Medicaid, and creates a new and innovative local . . . fund for uncompensated care.”

Williams-Kief countered that the letter is based on inaccurate information. He said Catania worked through the weekend to ensure that the money for alliance would not come at the expense of other programs.

Gray disagreed.

“We think our proposal is better,” Gray said in an interview.

Staff writer Nikita Stewart contributed to this report.