FIRST, on Jan. 20, President Carter said the United States would not support American participation in the Moscow Olympics unless Soviet troops were "fully withdrawn" from Afghanistan "within a month." But on Monday, White House counsel Lloyd Cutler said the matter could be left open perhaps until April or May. Mr. Carter's press secretary, Jody Powell, came right back yesterday to insist that the Feb. 20 deadline is still on.

But is it? How firm is the administration on an Olympics boycott, which it has been plugging around the world? There is always a certain amount of grumbling aboard about American inconstancy and the tendency to go it alone. The French -- who, to be sure, have made something of an art form of nit-picking American policy -- call it "le zigzag." But recently the administration has provided an unusually copious supply of grist for that mill. a

It is reported, for instance, that the administration did not consult France before announcing that France would attend the foreign ministers' meeting originally planned for Feb. 20, that it did not consult the allies before announcing its Olympic boycott plans, that it did not get around to notifying the allies when it finally decided to shelve sanctions against Iran, that it did not consult the allies when it announced, in their name, its new readiness to use force in the Persian Gulf.

The Europeans have not been exactly paragons of consistency or firmness in their reactions to Afghanistan -- though the recent Franco-German joint warning to the Soviet Union was impressive. Those American officials who, piqued especially by French criticism of erratic American behavior, responded by cataloging instances of erratic French behavior had a certain point. Many Europeans would like to believe that the Afghan affair will turn out to be analogous to the Soviet invasion of Czechoslovakia in 1968: it passed.

Yet an underlying point must be made. The Europeans are not insensitive to issues of their own security. Just three months ago they committed themselves, in the face of harsh Soviet threats, to the modernization of NATO's nuclear forces. But no Western European government can afford to be more anti-Soviet than the United States. They live too close, they trade too heavily, and they aren't big enough. A trade embargo, for example, is under discussion. For the American economy, it would be rather minor. But for the Germans, sales to the Soviet Union are an important proportion of the export trade. The Social Democrats have based 11 years of foreign policy on the assumption that detente with the East is consistent with the American alliance. West Germany, like the United States, is moving toward national elections, and the opposition is under stridently conservative leadership.

That is why Europeans are now anxiously trying to gauge the American mood. They wonder how much of the vehement American reaction to Afghanistan may be due to frustration over the imprisonment of diplomats in Tehran. If the hostages are released, or after the elections, will Americans return to an attitude of business-as-usual? To Europeans, that possibility commends caution in making any large or rapid changes in their relationships with the East. That is the central fact that American diplomacy can never afford to ignore.