THE BELIEF that New York City is a rehabilitated "miserable sinner," as Rep. Henry S. Reuss (D-Wis.) described it, may have had much to do with the size of the margin by which the House of Representatives passed a long-term aid bill Thursday. That margin - 92 votes - surprised even the most optimistic of the city's friends. Despite a massive lobbying effort by the Carter administration and a bipartisan group of New York officials, they had expected the bill to squeak through by fewer than half that many votes. But the city's top officials and financial advisers have made a persuasive case in recent weeks that it is on the road to financial recovery and that long-term aid is the appropriate way for the federal government to help it.

Sentiment on the Senate Banking Committee, to which the action now shifts, is not so clearly defined. Some of its members still seem unconvinced that New York City is deserving of further federal aid, and many seem to favor another short-term bail-out over the long-term approach voted by the House. But even some of those who have doubted all along the wisdom of a federal prop for the city's finances concede its officials have made a strong case.

In the three years since Mayor Abe Beame came to Washington hat in hand, both New York City and New York State have done much to clean up the mess that years of mismanagement had created. Above all else, they have kept the promises they made in 1975 when Congress provided the money necessary to let the city escape bankruptcy. Given the pressure generated by normal political activites and by inflation, that has been no small feat. The job is not finished, of course - far from it.

It seems clear to us that the city is entitled to continued federal aid. Its case would have been even stronger if its labor unions had been more receptive to cost-cutting proposals. But its new political leadership, Mayor Edward I. Koch and City Council President Carol Bellamy, understand what went wrong, and what is wrong, in the city's finances. They have given every indication of keeping it headed in the right direction.

If New York City is to get that further aid, it should be in the form that does the most good. Long-term federal guarantees of $2-billion worth of bonds would provide the city with the stability it needs to do the rest of the job. Short-term aid would merely keep it limping along for another two or three years, at the end of which, the odds are, its officials would be back in Washington confronting Congress with same choice it has now.

The process of financial rehabilitation in New York has gone far enough for Congress to believe the city when it says it has repented. Sufficient financial controls are in place so that a commitment to help it through the next 15 or 20 years is not just an act of faith. The Senate ought to join with the House in giving the biggest financial sinner in the history of American governments a fullopportunity to repent.