But soon the most serious challenge of all may arise: how Mr Clinton and his team will handle the increasing possibility of a nuclear confrontation in Asia. This threat has crept up on the President virtually unawares. Last spring he triumphantly announced that one of the world's last rogue would-be nuclear countries, North Korea, would be respecting the Non-Proliferation Treaty after all.
But now, after a disastrous trip to the region earlier this month by the US Defense Secretary, Les Aspin, it seems all too likely that the Great Leader Kim Il Sung, 81, and his son, the Dear Leader Kim Jong Il, 51, have every intention of goading the United States to the limit by pressing ahead with their nuclear ambitions.
On Friday, the State Department insisted that North Korea's latest, apparently conciliatory, statement conditionally offering to allow resumption of United Nations monitoring at its nuclear sites was a 'positive' sign.
But a spokeswoman for the International Atomic Energy Agency, meanwhile, was telling the Independent on Sunday: 'We can only surmise that our (UN monitoring) cameras have run out of film and the batteries are dead. We have no way of knowing what the next step will be as our inspectors have not been allowed back since August. There is a discrepancy between the plutonium that appears to have been produced and what they (North Korea) have declared as being produced. So far they have given us no satisfactory explanation.'
Intelligence reports show that 70 per cent of North Korea's 1.1 million-strong army is massed along the demilitarised border with South Korea, and that the Great and Dear Leaders' Scud missiles are within easy striking distance of Seoul - just 25 miles away. American F-16s are constantly screaming overhead in readiness for the unthinkable.
Last Sunday Mr Clinton added to the tension by saying that any attack by North Korea on the South, where the US has 37,000 troops, would be construed as an attack on the US itself. Democratic Congressman Gary Ackerman, just back from North Korea, is not the only one who finds it all rather frightening. 'My concern is that this thing is escalating a little bit too quickly,' he says.
In so much as the administration has any clear foreign policy, it is to keep hammering away at the importance of Asia. This is why, rather than visiting London, Paris or Bonn, President Clinton has already been to Tokyo and Seoul; Mr Christopher, during the administration's 10 months in office, has been to the region three times.
He explains that this is because in the post-Cold War era, the US has 'vital security stakes' in that part of the world, in which it has fought three major wars in the past 50 years. This week those United States interests will be further underlined when Mr Clinton flies to Seattle to meet his Asian counterparts for the Asia-Pacific Economic Co-operation Forum.
But precisely because it has made so much of the importance of Asia, the administration is coming dangerously close to boxing itself in; should the volatile and headstrong Great and Dear dictators now choose to provoke the US or its Asian allies (either through persisting with a nuclear programme or by some other military mischief), Mr Clinton is effectively committed to a big military response.
The flea would thus have provoked the lion into roaring, with dangerously unpredictable consequences.
Should American macho pride be ruffled by yet another petty tyrant, one South Korean official fears, both Koreas could go up in a Waco-style conflagration. And should North Korea persist with its nuclear malfeasance, then clearly South Korea, Japan and Taiwan are going to want to go nuclear too - with untold consequences.
If Mr Clinton is to remain true to his word yet avoid a military crisis, North Korea is going to have to back down, renounce its aim to 'reunify' North and South by 1995, drop its nuclear programme and admit that it has been lying over its plutonium production. As the Americans would say, it is going to have to eat crow.
The situation requires a coherent foreign policy with no American flag-waving bellicosity and, above all, delicate unemotional diplomacy. Mr Aspin, afflicted with heart problems, does not inspire confidence in his senior officials; Mr Christopher does so even less. Few in Washington have real confidence that the looming international crisis will be averted. It is almost enough to make one long for the days of George Bush and James Baker.