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The council on Tuesday narrowly shot down an effort by Mr. Brown to remove the $32 million measure from their priorities list, noting the late-emerging issue caused “heartburns” for several members.

Council members Jack Evans, Ward 2 Democrat, and David A. Catania, at-large independent, said the mayor should find the money on his own instead of requesting it of the council.

Mr. Catania said the city was showing its hand in negotiations with a managed-care organization that threatened to leave the public health care system because of underfunding of Medicaid reimbursements, and he was visibly upset by the proposed allocation.

Other members noted it was a serious public health care concern for the entire city, and not one branch of government.

“This was yet another example where the legislature and the executive came together to find a constructive solution to what otherwise would have been a monumental problem,” Mr. Gray said on Wednesday.

Wayne Turnage, director of the Department of Healthcare Finance, said Wednesday the actuarial tables governing rates for D.C. Medicaid and the D.C. Healthcare Alliance reimbursements were “unsound.” The problem was discovered shortly after he assumed office this year and, after an analysis, the seriousness of the spending pressure coincided with budget talks.

The mayor said he was glad the council was still in negotiations, “so that we had an avenue to be able to find a solution.”

“I think we took the most responsible avenue, and that is when something was discovered, we took steps to try to address it,” Mr. Gray said.

In a statement, the mayor praised the council’s “valiant effort” with its first budget vote to maintain funding for police officers and social services, before the health care pressure came to light.

“I wish that budgets were perfect,” Mr. Gray said. “I wish that when we did a plan we could say this is going to be executed exactly as it has been crafted, but it never works that way because this is a dynamic process.”