Of course Mayor de Blasio, card-carrying progressive that he is, supports setting up a government-funded single-payer health plan in New York, and declared as much in his State of the City speech on Thursday.

Just 48 hours earlier, though — and perhaps unwittingly — de Blasio made the best case yet that single-payer would be a colossal waste of time and money.

On Tuesday, the mayor went on national TV to announce that his administration will soon “guarantee health care for every New Yorker.”

Calling it the “most comprehensive plan in the nation,” de Blasio promised full medical care for 600,000 uninsured city residents — including undocumented immigrants — without need of state or federal legislation.

What’s more, he said he could do it for the low, low price of $100 million, mere rounding error in the context of an $89 billion city budget.

It turns out — surprise! — Hizzoner was engaging in a bit of hype. His plan is actually a relatively modest expansion of existing city services.

But he illuminated a timely truth: New York is closer to achieving universal access to decent health-care than is commonly understood. And the state, like the city, could close the remaining gaps without anything close to the massive expense and disruption that a Medicare for All-style single-payer system would entail.

After five years of Obamacare, the state’s uninsured rate has dropped to a historic low of 5% or so. Many of those who still lack coverage are poor enough to qualify for government-funded insurance through Medicaid or the Essential Plan, and could sign up tomorrow.

Everyone else — at least within the five boroughs — has the fallback option of using New York City Health + Hospitals, a city-owned network of hospitals and clinics that has a long-standing policy of charging only what people can afford.

De Blasio’s new proposal would steer some of the uninsured into MetroPlus, a city-run health plan. For those who can’t afford the premiums, he wants to do a better job of delivering free or reduced-price services through Health + Hospitals.

So his “guarantee” largely boils down to repackaging the safety net that the city has been providing all along.

But de Blasio plan also has the virtues of being doable, affordable and targeted to the people who most need help. Contrast that with the single-payer legislation being debated in Albany, known as the New York Health Act.

Rather than focusing on the roughly 1 million uninsured, it would force all 20 million New Yorkers to change to a new plan, operated and paid for by Albany. It would jack up taxes by an estimated $139 billion — much more than doubling the state’s already heavy tax burden. Plus, it would rejigger the revenue streams for every health-care provider in the state, with a destabilizing effect on access and quality.

By the way, only a small part of the massive price tag would go toward improving things for the poor and uninsured. Most of the $139 billion would be spent on reinventing the wheel for people who already have insurance, and who don’t necessarily want to change it.

The New York Health Act is the equivalent of a multi-organ transplant for a patient who would be better off with a course of antibiotics.

This is not to say that de Blasio’s plan is a sure-fire success. Health + Hospitals has been struggling with deficits for years, despite heavy taxpayer subsidies, and it’s unclear how it would afford an influx of even more patients who can’t pay their full bills.

Nor would this approach work the same way in other parts of the state that have no equivalent of the city’s government-owned health system. Upstate and on Long Island, any comparable guarantee would have to be delivered through private, not-for-profit health-care providers — which, after all, are supposed to provide charitable benefits in return for their tax-exempt status.

That would undoubtedly require more money and effort than de Blasio’s plan — but the challenges would be trivial next to the almost certain morass of single-payer.

Whether he intended to or not, the mayor has illuminated a saner path to universal coverage in New York State. Gov. Cuomo and the rest of Albany would do well to follow it.