The City Council on Thursday put its political clout behind a proposal in Albany to overhaul state health care by creating a “Medicare for all” program that would raise taxes by $139 billion a year.

The single-payer plan would extend coverage to the roughly 1 million uninsured New Yorkers — including undocumented immigrants — and eliminate all co-pays and deductibles.

But it would also boost payroll and other taxes, especially for the wealthy, and require the federal government to hand over Medicare, Medicaid and other medical payments to the state.

The Greater New York Hospital Association, which represents 140 hospital and health systems, joined several municipal unions to oppose the idea at a hearing of the council’s Health Committee.

The council was acting in an advisory capacity because it has no direct say in the matter.

GNYHA Vice President David Rich said that while his group supports the program’s goals, it worries about a lack of federal funding, potential reductions in payments to hospitals and the estimated $139 billion a year in new revenues the state would need by 2022.

“There are huge obstacles in the way . . . and we do not believe these obstacles can be overcome,” he said.

A meeting of the bill’s Albany sponsors with municipal labor leaders sparked other concerns from union heads, who for decades have negotiated generous healthcare benefits into their contracts.

Henry Garrido, director of District Council 37, the largest municipal union, said he has made it clear the legislation would have to be changed.

“DC 37 has always supported universal health care but we have serious concerns about various aspects of the bill as currently drafted, and we have expressed those concerns to lawmakers.” he said.

Assemblyman Richard Gottfried (D-Manhattan), one of the bill’s sponsors, said he has already taken union concerns to heart and would rewrite the bills.

“Our parents didn’t raise us to screw workers. Period,” he testified at the hearing.

Gottfried said that even with the added costs of extending coverage to the uninsured, his plan would yield a net gain of $19 billion ­annually.