“It still boggles my mind that this is the same guy who goes, and sits down in front of that TV, and in front of you all in Albany, lays it all out, smartly and ably,” Mr. Rivera said, praising the governor’s coronavirus performance. “And then he breathes in, and the next thing that comes out of his mouth, ‘And you got to let me cut the Medicaid system.’”

As part of the budget negotiations, the executive branch provided the State Senate with data showing how hospitals could be affected by the proposed cuts; each senator then received an email detailing the impact on hospitals in their districts, Mr. Rivera said.

Many of the hospitals that would be hurt by the cuts are so-called safety-net hospitals, which largely serve uninsured or undocumented residents, some of whom are considered susceptible to infection because of cramped living or work conditions.

Indeed, the brunt of the proposed cuts at St. Barnabas, where almost 90 percent of patients are partly covered by Medicaid, could come from reducing $7.7 million in Indigent Care Pool funds, grant money meant to reimburse hospitals for treating poor and uninsured patients for free.

Dr. Perlstein, who complimented Mr. Cuomo’s response to the coronavirus, said it was unconscionable to grapple with the prospect of a funding cut “when we’re 14 days from Armageddon.”

“Especially at a time I’m asking my staff to give it all,” said Dr. Perlstein, who has worked at the hospital for over 20 years. “If these cuts remain, I have no way to survive as a hospital. I’m already walking a very fine line when it comes to revenue.”

Robert Mujica, the state budget director, said that it was “disingenuous” to scrutinize any individual hospital cuts without taking into account “the full picture” of other savings and efficiencies from the proposals, which he stressed are still being negotiated with the Legislature.