THE BILL to strengthen the International Monetary Fund was supposed to come to a vote in the House last week. But at the last minute Speaker O'Neill pulled it back, for the very good reason that there were not nearly enough votes to pass it. The leadership of both parties supports it. The opposition is a highly diverse mixture of old isolationists, new leftists, people who believe (wrongly) that the IMF is a front for the banks, and people who are trying to extract other concessions from the administration. At the moment, that opposition is the majority.

The tradition of voting against anything that looks like international cooperation is deeply embedded in part of the Republican Party in the House, and that is the central threat to this bill. Mr. O'Neill has warned the administration that the Democrats are not in a mood to exert themselves to pass it for Mr. Reagan over the opposition of his own party. The test for Mr. Reagan this time is not whether he can carry enough Democrats with him, but enough Republicans.

Why vote for this bill? The IMF is an international agency that borrows from its member governments and lends the money back to those that are in trouble. The present bill would increase by $8.4 billion the amount the United States can lend to the fund. Each of those dollars would be matched by about $4 in other currencies from other countries. The IMF generally lends in packages requiring commercial banks to increase their own loans. As the IMF once said, it does not bail out commercial banks--it keeps bailing them in.

If the United States does not support this kind of international cooperation, it runs a very high risk that in the next crisis--like Mexico's near-default last August--it will have to come to the rescue entirely with its own money. Which is preferable, contributing one-fifth of the rescue money or all of it?

Without a vigorous and continuous effort to strengthen the world's monetary system, the chance of defaults approaches 100 percent. A default by any of the larger Latin American debtor nations would have two immediate effects in this country. It would shut off an important market for U.S. exports and, by shaking American banks, it would mean higher-than-ever interest rates. If frightened banks then began refusing any more foreign loans, as some of the smaller ones have already, trade would begin spiraling rapidly downward. The last time that happened was in 1929-33, when America's unemployment rate rose to 25 percent.

The world's structure of trade and finance is immensely productive, but it is not stable. It does not balance itself. It has to be managed. An essential part of that job of management now falls to the IMF, which needs larger resources to ensure that it can meet its responsibilities in the tricky passage ahead.

No country has a greater interest in its success than the United States, the world's leading trader. Mr. Reagan is absolutely right to want the IMF bill passed. The question is how badly he wants it. To get it, he and the people around him in the White House are going to have to work a great deal harder among the congressmen of their own party than they have done so far.