Gov. Cuomo may be about to turn on New York big time — to boost his political support from the construction unions.

The pro-labor group #CountMeIn this month announced that Cuomo not only backs a bill forcing builders to use union labor and pay union wages, even on private work, but that, in fact, he has already “proposed” it: “Thank you @NYGovCuomo! Who has proposed legislation designating all work at Hudson Yards as prevailing wage,” it tweeted.

The bill cites projects — at Hudson Yards, Amazon’s site in Queens, the Gateway tunnel and on Roosevelt Island — to be deemed “public work” and made subject to “prevailing wage” laws.

Remember: Prevailing wages are not the same as the state-set minimum wage; they’re generally equivalent to union rates, which are far higher.

Applying prevailing-wage laws to firms doing work at those sites would undercut any edge they have in using nonunion labor and paying lower wages.

In other words, the unions think, if you can’t compete on price, no worries: Just get Albany to force up your competition’s price.

True, the tweet might be premature: Crain’s notes that it was the AFL-CIO that drafted the bill, and it has no sponsors. And a Cuomo aide refused to confirm the claim. Alas, the flack didn’t deny it, either.

Recall, too, that Cuomo has done plenty of favors for the construction unions — insisting, for example, on a $60-an-hour wage minimum for workers on developments that get tax breaks in exchange for subsidized housing.

You can’t blame the unions for wanting a bailout. But average New Yorkers would suffer: By forcing up wages and strengthening union monopolies, the law would guarantee less development and higher real-estate prices, including rents. Albany shouldn’t go along.

Indeed, if Cuomo tries to push it through, it would be one of the most glaring examples of him thumbing his nose at everyday New Yorkers to advance his own political standing with labor.

Should it pass, it could put funding for vital projects, like the Gateway tunnel and affordable housing, at serious risk.

Real Estate Board of New York head John Banks says it would “raise costs, limit job growth, reduce economic activity and ultimately have a harmful impact on New York.”

Labor clearly drafted the bill because it sees the writing on the wall: Its lock on the construction market is waning. REBNY notes that nonunion labor already accounts for 70 percent of residential work in the city.

Plus, Related Cos., the Hudson Yards developer, recently struck a deal with the carpenters union to allow more flexibility on hiring. Other unions may follow.

Yet Albany — Cuomo in particular — is supposed to protect the public, not aid ailing unions. The fact that his office won’t even comment here may mean he just doesn’t care.