The impression is that Vice President George Bush is being suddenly rushed into the European breach to do propaganda battle with the Soviets--to grapple for the hearts and minds of European peaceniks. And that's partly true.

But his European tour was actually in the active planning stage late last year. The idea was that early 1983 might be a good time for a top administration figure to be rallying and reassuring our allies on the most urgent arms control issue: the decision by the North Atlantic Treaty Organization in 1979 to deploy medium-range nuclear forces in Western Europe by the end of this year, in the absence of an agreement with the Soviets controlling the number of such weapons on both sides of the line.

What's happened is that the original, stately grand tour has been electrified by recent developments: the U.S.-Soviet war of words over arms control, the dangling of compromises and hints of counter-compromises and the big shakeup of the U.S. arms control apparatus. All this offers Bush a wealth of opportunities for easing European public anxieties, sorting out the sometimes conflicting thinking of allied governments and reaffirming Ronald Reagan's dedication to arms control.

An equal opportunity exists, however, for the careless (or misread) phrase or gesture that could make things worse.

And so, from conversations with those involved in the preparations, one comes away with a sense that, not necessarily through any failings on his part, George Bush is suiting up for Mission Almost Impossible.

The heart of the arms control problem right now is Europe's perception of Ronald Reagan's readiness to be reasonable. A substantial body of European opinion suspects that the U.S. president still hankers to run the Soviets into the ground economically (showing up the fatal flaws of communism in the process) by more than matching them in military spending and deployments. So, according to his aides, Bush will present himself as the man who knows Ronald Reagan better than just about anybody --and thus the man best positioned to testify to his boss's determination to bargain in good faith.

But Bush cannot illustrate the point while Ronald Reagan is holding fast to his famous "zero-zero" proposal. This would have the Soviets dismantle all their medium-range missiles as the price for an agreement by the Western allies not to deploy in Western Europe a new generation of Pershing II and cruise missiles capable of reaching the Soviet Union.

The new top man in the Kremlin, Yuri Andropov, has dangled a seductive compromise that would cut the Soviet medium-range forces down to the level of the combined French and British independent nuclear forces. It's a non- starter-- but a show of seeming flexibility. Bush will have nothing comparable to show, other than a public suggestion of the obvious: that there may be some give in the U.S. position if the negotiations in Geneva show serious signs of movement.

"We are not going to get into negotiating or come up with some new offer," says former four-star admiral Dan Murphy, Bush's chief of staff. Rather, Bush will be compelled to convey U.S. determination to proceed with deployment of the intermediate-range nuclear forces on schedule, absent an agreement with the Soviets. Since some of them are supposed to be operational by December, this means serious installation work will have to begin this summer. Even to suggest slippage in the timetable would rob the United States of leverage in the Geneva talks.

Yet in West Germany, where elections are due in March, a recent poll shows that 65 percent of the public wants to renege on the 1979 two-track decision and delay deployment even if no progress has been made with the Soviets.

On the face of it, taking the firm line would seem to favor West German Chancellor Helmut Kohl, who is alone among Germany's leaders in sticking by Reagan's "zero-zero" position. But in practice it may work the other way: not only the socialist opposition but Kohl's supposed political ally, Franz Josef Strauss, are pushing for compromise. There are also hints of softness in Italy's position. Britain's Prime Minister Margaret Thatcher has suggested there might be some merit in looking at an agreement on "balanced" forces on both sides.

So Bush is "going to be doing a lot of listening," says Murphy. He would like to bring back to the president and other policy-makers the best fix he can get on European attitudes. He intends to dwell heavily in public on common aims, interests and values.

Bush will promise consultation, exude camaraderie. In two major speeches (in Berlin and London) and no end of private talks, he will weigh his every word.

If his mission is almost impossible, it is also unavoidable. If nothing else, it will provide a necessary measure of the depth of the crisis in Western alliance affairs.