Gov. Andrew Cuomo’s response to the Empire State’s big Medicaid deficit, as laid out in his budget presentation on Tuesday, was a disappointing mix of delay, deflection and delegation.

In an especially concerning development, Cuomo’s budget director, Robert Mujica, left the door open to hiking taxes on health insurance as a way to close the gap.

Medicaid — a state-run health plan for the poor and disabled that covers some 6 million New Yorkers — is running $4 billion over budget in the current fiscal year and faces a projected gap of $3.1 billion in fiscal year 2020-21, which starts April 1.

The Cuomo administration said in November that it would partially close the gap by cutting $1.8 billion right away. Yet on Tuesday, Cuomo lowered the immediate savings target to $599 million and said he would make up the difference with cash on hand, ­including unexpectedly strong tax receipts. This effectively delays harder decisions for at least ­another few months.

The governor also elaborated on his claim, first leveled in his State of the State speech, that ­local government should take the blame for spiraling Medicaid cost. This is mostly a deflection from his own larger share of the fault for what has happened.

Cuomo’s argument is that local officials play a role in determining who gets how much in Medicaid benefits yet have no “skin in the game,” because their local contribution to the program was frozen in 2015.

It’s true that officials in New York City and the 57 counties make key decisions about who qualifies for long-term-care services, and that part of Medicaid has been growing particularly fast. But New York was an outlier on home-based, long-term-care spending since long before Cuomo became governor, so it is far from clear that freezing the local share has made much of a difference.

Meanwhile, Cuomo has been making costly policy choices of his own. He pushed through a minimum wage hike, to as high as $15 an hour, that has added $1.5 billion a year to the state’s Medicaid tab.

In the fall of 2018, when Medicaid was already over-budget, Cuomo’s Health Department ­ordered across-the-board rate increases for hospitals and nursing homes. And it was Cuomo’s Budget Division that delayed $1.7 billion in payments from fiscal 2019 to fiscal 2020, which directly led to the current deficit.

Instead of addressing these ­issues, the governor proposed to rein in the behavior of local officials with a carrot-and-stick scheme: Localities in which Medicaid costs rise faster than 3 percent would be billed for the overage, while localities that hold costs below 3 percent would be rewarded with 25 percent of the savings.

New York City and the 57 counties will undoubtedly ­oppose any attempt to shift costs to them, and Cuomo’s scheme seems unlikely to get far in the Legislature. But if local officials are being too loose with the state’s money — which is possible — then why not have the state take full control over the ­eligibility decisions?

Cuomo’s budget for the next fiscal year counts on shaving ­another $2.5 billion from Medicaid’s spending growth, but ­offers no details on how that will be accomplished. Instead, he is delegating the job to a reconstituted Medicaid Redesign Team, a panel of health-care industry stakeholders to be co-chaired by Michael Dowling, head of the Northwell Health hospital system on Long Island, and Dennis Rivera, former chief of 1199 Service Employees International Union, the state’s largest health-care union.

There is reason to be skeptical that the likes of Dowling and Rivera will willingly cut their own funding, but this structure worked reasonably well, at least during Cuomo’s first term. Its early success depended on the threat that the governor would make his own cuts unilaterally if the panel fails to recommend adequate savings — authority Cuomo has never ­actually invoked and didn’t emphasize this time around.

In a later briefing for reporters, Mujica, the budget director, was asked if the Medicaid Redesign Team would have the ­option of hiking taxes on health insurance to close the gap — and he didn’t rule it out.

This would be an expensive outcome for average New Yorkers, who already pay $5 billion a year in surcharges levied through the Health Care Reform Act — which are the state’s third-largest source of revenue and one reason why it has the highest health premiums in the lower 48 states.

Cuomo has said in other contexts that he would oppose raising taxes to balance this year’s budget. If that’s the case, he should take HCRA hikes off the table.