ALBANY — The teachers’ union has ramped up its war against Gov. Andrew Cuomo’s budget plan, releasing a poll Monday saying New Yorkers overwhelmingly back tax hikes on the rich instead of service cuts.

The pro-tax-on-the-wealthy findings released by New York State United Teachers comes just days after city teachers’ union leader Mike Mulgrew summoned lawmakers to a closed-door strategy session to fight Cuomo’s plan to shift more of the growing costs of the massive $77 billion Medicaid program to the Big Apple and other localities.

The union-financed poll of 1,000 registered voters found that 90 percent or more support a 2 percent tax on billionaires, increasing the income tax on residents making more than $5 million a year, and imposing a tax on luxury homes worth more than $5 million that are not a primary residence.

The survey said 72 percent of voters were more likely to vote for a candidate who favors passing these taxes on millionaires compared to 9 percent who wouldn’t.

The support for taxes on the rich were backed by large majorities in every region of the state — 76 percent in NYC, 70 percent in the suburbs and 68 percent upstate. The pro-tax sentiment included 61 percent of Republicans and 65 percent of unaffiliated or independent voters, as well as 80 percent of Democrats, the poll said.

The survey was conducted by Hart Associates, a firm long on retainer for the teachers’ unions.

The main dispute in the unions’ resistance to Cuomo’s budget plan is his proposal to cap state spending on Medicaid, the government-funded health insurance program for the needy.

Cuomo’s plan would cap the growth in Medicaid to 3 percent to close a projected $4 billion shortfall in the Medicaid program. The city and other counties would have to pay for any costs above 3 percent.

Having to foot a bigger bill for Medicaid could mean less money for schools and other programs, United Federation of Teachers president Mulgrew argues.

“Why am I doing this? I stand up for New York City,” the union boss told The Post.

“You keep fixing the budget in Albany by shifting costs to municipalities. It’s ‘I balance the budget by making you pay for it.’ Enough of this,” Mulgrew said.

Mulgrew hosted the extraordinary meeting at UFT headquarters in Lower Manhattan on Friday afternoon, and it was attended by city Comptroller and mayoral candidate Scott Stringer, Council Speaker and mayoral candidate Corey Johnson, Public Advocate Jumaane Williams and numerous state lawmakers and City Council members.

Stringer and Johnson attended the Albany noon press conference where the teachers’ union released the tax poll findings.