Showdowns around world turn all eyes toward the White House

Like a juggler the administration is keeping about half a dozen crises in the air at the same time.

* In Geneva Soviet leaders threaten to walk out of the nuclear disarmament talks if NATO allies deploy more missiles in Europe. A superpower showdown seems only a month or two away.

* In the United States, patriotic reaction endorses President Reagan's Thursday broadcast in which he defended the double crisis in Lebanon and Grenada.

* Efforts continue to find a peace formula for distracted Lebanon, where a new diplomatic encounter among rival powers is attempted in Geneva.

* Congressmen ask for a part in the international negotiations and Congress considers an invocation of the war powers resolution that would require the President to bring back troops from Grenada within 60 days without further approval by Congress.

Short of wartime, such stirring scenes have rarely been seen in Washington. The briefing room at the White House is constantly watched by reporters. On the greensward outside, as many as five spots are preempted at one time for waiting TV tripods, cables, and cameras for itinerant interviews with domestic and international callers.

Background for this is a succession of crises.

Soviet-American relations have deteriorated and some feel a showdown is imminent. In September there was the brutal downing by Soviet interceptors of a Korean airliner that had strayed over Russian territory. Then, there was the suicide bombing in Lebanon which killed more than 200 sleeping marines, and a similar attack on the French peacekeeping force. Next came the outbreak in Grenada with invasion by the US Marines and airborne troops that drew worldwide attention and controversy.

Amid this was the continuing confrontation of nuclear deployments in Europe with each side making threats and suspense rising as in a theatrical performance.

Even those who criticize US policy in Lebanon and Grenada acknowledge the eloquent character of President Reagan's dramatic presentation. Few presidents have appealed so firmly to the public. He related with deep emotion the heroism of a wounded marine invoking the corps motto ''Semper fi(delis)'' (always faithful). The speech brought one of the broadest waves of support to the White House in recent years.

Washington is accustomed to such outpourings, however. Observers warn that it is the more considered later judgment that is more lasting: President Carter, for example, originally got an overwhelming approval to his efforts to rescue hostages in Iran. Later it evaporated.

Now the questions being asked here are how long will the Grenada operation last, what will be the cost in lives, and perhaps more important, what will be the world's overall impression of the stability and wisdom of the United States acting as international policeman.

Congress is still to be heard from. And it appears that the Reagan speech will not stall a drive to bring the War Powers Act to the front.