NOT SO LONG AGO, the word from New York was that the city couldn't possibly balance its budget this year and that it and the nation would go through another exercise in financial brinksmanship sometime this summer. So a certain skepticism greeted Mayor Abraham Beame's announcement that not only could the budget be balanced but also that some taxes could be cut and a few new employees added. The skepticism, it turns out, is justified. The city's budget is balanced only if you acccept a couple of assumptions that your own banker probably wouldn't accept if you tried to fly them past him.

Mayor Beame is counting on congressional passage of a counter-cylical revenue-sharing program that would provide New York with $135 million in aid. He is also counting on working out a method to defer the payment of $250 million in debt charges. Even if he proves right in assuming these things will happen - and you have to admit he has been exceptionally lucky in the past couple of years with some equally hazardous assumptions - his own figures show that New York goes back into the red after next fiscal year. In addition, those 6,000 employees he wants to add to the city's payroll in the next year will be paid out of federal funds under a job-training program.

Even if you accept Mayor Beame's budget assumptions, all you can conclude is that New York has found a brief respite. Its financial problems are not over and the prognosis remains grim. The business taxes that the mayor has chosen to cut may help stem some of the city's general economic decline. And the handful of expanded programs he has included in the budget may provide a spark of hope. But unless the federal government decides to be far more generous in aid to urban areas than it has been in the past, the problem of New York has merely been put off for a year or two.

Nevertheless, Mayor Beame does deserve credit for taking some major steps in straightening out the city's financial situation. The record of reduced payrolls, cuts in programs, and improved fiscal responsibility over the last two years is impressive. It may be true, as the mayor claims, that the city cannot cut much more out of its spending without digging into services that he believes New Yorkers regard as essential. If such is the case, he - or his successor - will have even more difficult problems in the future. In the meantime, however, Mayor Beame has bought some time in an election year, and that needs to be kept in mind in considering what this budget really means.