IN NEW YORK, it is being said that Gov. Hugh L. Carey has pulled off a political coup of the first magnitude. By proposing to cut state taxes by $750 million, he has outflanked his political opponents and created the centerpiece of a political campaign should he chose, as everyone thinks he will, to run for reelection. What he has done, no doubt, is good politics - in traditional terms. But it may not turn out that way if this tax cut brings down the house of cards on which the finances of New York City now rest.

Gov. Carey's rationale, which seems to have sweeping support in the state legislature, is that New York's high taxes are stifling economic development. By reducing taxes, he hopes to stimulate the economy, thus generating more revenue at lower tax rates in the long run. He may well be right - in the long run. But hanging over the state of New York, in the short run, is the financial condition of New York City. That condition, despite three years of austerity and outside aide, is not good. The city is still running and annual deficit of somewhere between $250 million and $1 billion, depending upon whose figures you believe. Its credit rating isn't worth mentioning. And the rescue operation that has kept it afloat for the last three years is about to end.

There is considerable disagreement among politicians and financial experts about the form that rescue operation should take after June 30. But there is no disagreement about the fact that the city must have some kind of continuing aid - from the banks, pension funds, the state of New York, the federal government or some combination - if it is avoid defaulting on its debts later this year. By going for a tax cut instead of using the state's surplus to help the city, Gov. Carey is ruling out one source of the necessary aid and jeopardizing at least one of the others.

We can already hear the questions in Congress.Since New York state is not doing its utmost to help, why should the federal government continue to provide short-term loans to New York City, as Gov. Carey wants it to do? Why should the federal government help the city rearrange its long-term debt, as more sophisticated financial analysts say it must? Why should the federal government make the prevention of bankruptcy in the city "the single object of urban policy," as New York Sen. Daniel P. Moynihan is demanding? We would not like to be in the shoes of Gov. Carey and Mayor Edward I. Koch when they try to answer questions like those before a Senate committee whose two ranking members have already concluded that the federal government should provide no additional loan aid.

Of course, it is possible, as Sens. William Proxmore (D-Wis.) and Edward Brooke (R-Mass.) contend, that New York City can handle its own immediate financing problems without aid from Washington as long as the state, the banks and the pension funds cooperate. But even if an arrangement without federal participation can be worked out so that the city squeaks past it debt deadlines, it long-range prospects are dim. Felix G. Rohatyn, the financial expert who has been deeply involved in the bail-out operation, says the city cannot survive without substantial budgetary help from Albany or Washington. If he is right, and we suspect he is, Gov. Carey's tax cut creates an enormous risk. It eliminates the state treasury as a source of that aid, at least until the governor's hoped for economic boom occurs, and it undermines the chances of getting that aid out of Washington.

In the unlikely event that Gov. Carey can pull off the whole package - a tax cut and new federal loans as well as additional federal budgetary aide - his action will indeed, be a political couP. If he can't do that, it is likely to come back to haunt him. Unless, of course, the governor is ready to wash his hands of New York City and dump its problems on Washington - or is prepared to see the city, sooner or later, go bankrupt.