From the moment of its unveiling at the start of the year, Gov.  Andrew Cuomo’s “free” college tuition plan seemed to have been hastily reverse-engineered from a campaign slogan — a Bernie Sanders presidential campaign slogan, that is. The governor did nothing to dispel that impression when he invited the Vermont senator to deliver an endorsement of the plan when it was first rolled out at a Queens College rally on Jan. 3.

News coverage of the proposal generated the kind of headlines the governor no doubt hoped for — bolstering his claim of having sponsored a bold “first in the nation” program for students from families earning gross incomes up to $125,000.

In reality, both as originally proposed and as modified by the new state budget adopted this week, Cuomo’s “Excelsior Scholarships” initiative isn’t nearly as broad and generous as the governor made it out to be. Among other things, recipients have to take a full course-load, and graduates must promise to stay in New York for at least as many years as they received the scholarship.

But the strings attached to Cuomo’s tuition program are just about its only redeeming features.

After all, there’s no such thing as “free.” Cuomo’s program will have to be paid for by a combination of higher taxes — including taxes paid by parents of students getting the new scholarships — and by higher tuitions for SUNY and CUNY students who aren’t in the program. Indeed, the final state budget also authorizes a $200-per-year tuition increase over each of the next four years. On top of that, students living on campus will still need to pay room and board charges totaling two to three times the tuition.

In the adopted state budget, the initial appropriation for the program is capped at $87 million — plus $19 million to provide added scholarships roughly half as large, on a more restricted basis, to students in private colleges and universities. If that money isn’t enough, scholarship recipients will have to be selected by lottery.

A wide-open entitlement truly offering “free” higher education for the majority of middle-class New York high school grads would have been a massive budget-buster. Keep in mind that SUNY and CUNY are already a bargain, with average tuition and fees well below average, ranking 39th out of 50 state public university systems. And New York’s Tuition Assistance Program (TAP) already spends nearly $1 billion a year to provide a genuinely tuition-free ride to low-income students, plus a decent tuition subsidy for the near-poor.

Instead of expanding the time-tested TAP model, Cuomo invented a completely new program with a design difference that’s also a major flaw.

TAP and other need-based government programs target benefits to students based on taxable income, net of exemptions and deductions—which is more reflective of ability to pay. Such programs also gradually reduce benefits as income increases above some maximum level.

That’s not the case with Excelsior Scholarships, which when fully phased in after three years will extend eligibility for “free” tuition to all otherwise qualified students from families earning up to $125,000 in adjusted gross income, regardless of family structure or size or place of residence. The inequity of this approach should be immediately obvious: a $125,000 income will take you a lot further upstate, especially if you have just one college-age kid and a paid-for house, than it will in the New York City metro area, especially if you have a larger family and a big mortgage.

The crude income limit includes a sharp cutoff: if your gross income exceeds $125,000 by even a dollar, you are ineligible.

Meanwhile, the message sent by Cuomo’s higher education policy — and by his continued allocation of billions of dollars to porky “economic development” projects — will actually undermine any case he tries to make for better treatment from Washington.

Cuomo has been loudly warning that federal Medicaid, Obamacare and federal tax reforms favored by House Republicans would be devastating to New York, costing the state billions of dollars. Yet even while hyping his “college affordability” initiative, he’ll be demanding a break from Senate and House members whose state university systems, for the most part, charge higher tuitions than New York’s.

The governor ought to relish those news headlines about New York’s “free” college tuition while he still can. Soon enough, Republicans in Washington will be waving them in his face.