Just when it looked like New York’s free-spending public schools were about to do some serious belt-tightening, along comes the US Senate this week to clear the way for another $26 billion “stimulus” dose, including $600 million for K-12 education in the Empire State.

This will be enough to undo a large chunk of the $1.4 billion school-aid cut that Gov. Paterson fought to preserve in the recently enacted 2010-11 state budget. The federal aid package also includes roughly three-quarters of the $1 billion in extra Medicaid reimbursements Paterson was counting on to help balance this year’s budget, plus $400 million in Medicaid funds that will flow directly to New York City.

Sens. Charles Schumer and Kirsten Gillibrand, both on the ballot this year, now get to bask in the media afterglow. “DC Coming to NY’s Re$cue,” as one headline put it.

A few more “re$cues” like this and we’ll be really broke.

The state, the city and local school districts have burned through about $17 billion in federal stimulus funds, including amounts budgeted for this year. Assuming the next round of state and local stimulus wins House approval next week, the result will be even more spending that New York taxpayers can’t possibly sustain — and that Washington can’t indefinitely subsidize.

Keep in mind:

New York’s school spending of $17,173 per pupil as of 2007-08 was the highest of any state — 67 percent above the national average, according to the latest Census Bureau data.

Between 2000-01 and 2008-09, New York schools added 14,746 teachers and 8,655 nonteaching professionals — even as enrollment was dropping by 121,280 pupils.

Confronted with an average 5 percent state-aid cut, school districts tapped their reserves, trimmed programs and held down tax hikes in their proposed 2010-11 budgets. As a result, voters in May approved 92 percent of school budgets. For the most part, schools and the public signaled they could live with the aid reduction that congressional-stimulus fans portrayed as destructive and intolerable.

Mayor Bloomberg announced in June that he’d avoid layoffs in New York City schools by withdrawing his offer of a pay hike for city teachers. The city’s share of the education stimulus, estimated by Bloomberg at $200 million, could eventually find its way into the teachers’ pockets — expanding the base of costs that must ultimately be borne by city taxpayers.

Next year’s state budget gap of at least $7.5 billion can’t be closed without further cuts in education aid, which comprises a third of state-funded expenditures. Schools can’t put off the inevitable, even if Schumer & Co. would like to pretend they could.

Congressional Republicans who opposed the latest stimulus measure are right on the money when they point out that the new package — including funds that must be spent to rehire teachers or sustain payrolls — is an enormous gift by Democrats to their public-employee union allies.

It will reward the recalcitrance of unions in such places as the struggling city of Yonkers, where school officials this year offered teachers a one-year contract extension in exchange for a temporary wage freeze that would save $16.5 million, enough to preserve hundreds of jobs. The union president dismissed the overture as a “nonstarter.”

Yonkers teachers have now pocketed their 3 percent raises for 2010-11 — on top of 12.5 percent in base-pay increases over the last three years. So the district may end up using any new federal aid to restore, for one more year, some of the jobs it will remain unable to pay for a year from now.

Elsewhere around the country, the Web site Education Intelligence Agency reports, school districts were already rescinding announced layoffs before the stimulus bill was resurrected. More cash from Washington will simply be a wasteful windfall.

Lt. Gov. Richard Ravitch pointed out in a Wall Street Journal op-ed earlier this year that federal stimulus aid had come with strings that prevent states from economizing in areas such as education and health care.

“The federal stimulus has led states to increase overall spending in these core areas,” he wrote, “which in effect has only raised the height of the cliff from which state spending will fall if stimulus funds evaporate.”

And evaporate they will, sooner or later.