The bizarre spectacle - two Bill Clintons in the space of a few seconds - was the more bizarre for being a precise reversal of the double persona of his predecessor. George Bush was always fascinated by the rest of the world but bewildered and bored by his own country.
Just when Bill Clinton's popularity ratings have been recovering dramatically, he faces the most perilous crisis of his young presidency. Nothing is more calculated to enrage the American public than the sight of their soldiers being killed and humiliated in a foreign land - especially when their reasons for being there are not absolutely clear.
The Texan Republican, Senator Phil Gramm, forgetting that it was Mr Bush who began America's 'humanitarian' mission in Somalia, growled last week: 'The people who are dragging American bodies (through Mogadishu) don't look very hungry to the people of Texas.'
Just as he seemed about to seize control of his own agenda for the first time, Mr Clinton finds himself haunted by the spectres of past debacles. Ronald Reagan abruptly withdrew troops from a peace-keeping mission in Beirut in 1983 after a suicide lorry-bombing left 241 US marines dead. Mr Reagan survived but Mr Clinton's two immediate Democrat predecessors saw their presidencies destroyed on foreign shores: Jimmy Carter by the Tehran hostage crisis and Lyndon Johnson by Vietnam. Somalia contains, in miniature, echoes of all three.
It is a moment for Americans to ask again whether Mr Clinton, nine months into his White House tenancy, has the 'right stuff' to be their president. When he appears before them in the Oval Office, as he did on Thursday evening to explain his Somali policy, does he inspire trust and respect? Can he show, or at least convincingly act out, leadership in the way that Ronald Reagan and George Bush often could?
Despite the trappings and pomp that now surround him, Mr Clinton did not convince. Even on the most serious occasions, he seems unable to shake off that goofy, aw-shucks smile that makes him look more like a schoolboy who has just won the class prize than a commander-in-chief. And Bill Clinton, who avoided Vietnam and wrote that he detested the army as a young man, has never been able to look comfortable alongside the military. A Clinton salute is more likely to elicit smirks from voters than feelings of patriotic pride.
Most damaging, perhaps, is the enduring perception of the President as a 'Slick Willie'. His transparent desire to please everyone only works to confirm the popular suspicion that he has no particular commitment to anyone.
On foreign policy at least, his leadership seems to be utterly reactive. On Somalia, the impression is that he was driven into explaining his position by an outraged Congress. When it came, his solution was classic Clinton: he is not pulling his troops out nor is he responding with massive force. Instead he is trying to do both, by doubling the American presence now and promising to be out by next April. Only when he addresses domestic policy matters, most notably in presenting his plan for healthcare reform to Congress last month, does Mr Clinton appear equal to his office.
One Washington foreign policy analyst, an acquaintance of the President, says: 'Bill Clinton's entire persona, his self-image as a politician, depends on his being able to outstrip every other politician in knowing about the domestic issues . . . On a scale of 1-100 you would give most politicians about 60, but Bill Clinton gets about 90. On foreign policy, though, I would say he is at 30. I suspect he feels that if it cannot be 90 then he will not even try to make it to 60.'
Clinton foreign policy has been marked by muddle, punctuated by bursts of incoherent energy, relapsing once again into muddle. His staunch support for Boris Yeltsin through the Russian crisis seems a notable exception. But the policy was in essence a non-policy: holding onto Boris for 'fear of something worse'. There was near panic in Washington, as well as the Kremlin, when the anti-Yeltsin forces were briefly in the ascendant last weekend.
'The fundamental problem is that there is no rudder,' the former Secretary of State, Lawrence Eagleburger, said in an interview with the Independent on Sunday last week. 'They're going from pillar to post. Bosnia is the clearest example and now we're getting it on Somalia. They're back and forth and it is very hard to know what they're doing or exactly what it is they're aiming at on a lot of the issues.'
Nor were there favourable reviews for a string of speeches made last month by cabinet officials to rebuff claims that the administration had no post-Cold War vision. There was particular disappointment with the President's vaunted address to the UN General Assembly in New York on 27 September. While reassuring the diplomatic community that America was not about to turn in on itself, Mr Clinton exhorted the UN to restrain its appetite for involving itself in every conflict on the globe.
'It was an opportunity for a major presentation of the UN's objectives and what it should be doing,' Mr Eagleburger remarked. 'Instead we got what it shouldn't be doing. The world is going to be an awful mess and you don't approach it by saying what you are not going to do.'
Critics, including Mr Eagleburger, concede that with the old bi-polar world of the superpowers gone, it is hard for any government to define a coherent foreign policy. 'It is an unpleasant and difficult and confusing world,' Mr Eagleburger said. And if the Bush administration were still in power? 'I think frankly we would have done it better. But I can't deny that we would have been confused too.'
A Western diplomat in Washington was similarly sympathetic. 'It's not surprising (Clinton) doesn't have an overarching concept of what to do because for the life of me I don't know anyone in the world who does. Crises emerge without rhyme nor reason.'
Much of the problem can be traced to the President's unimpressive foreign affairs team. Warren Christopher, his Secretary of State, has drawn criticism from the start as a man of competence and caution but little imagination. The western diplomat said the President 'lacks a public figure in the foreign affairs arena who can get up and say in clear and impassioned terms what we're doing and why we're doing it'.
The President strove for the necessary clarity in addressing the nation on Thursday, as if grasping for the first time an American political truism: presidencies cannot be made by foreign actions or inactions, but they can be destroyed by them. Unless Mr Clinton can deliver on his promise to end America's involvement in Somalia tidily - which will have to include retrieving at least one hostage - he risks paying a heavy price indeed. Somalia is not Vietnam, nor is it Tehran. But the memories of both episodes are branded still on the American conscience. If Mr Clinton takes the country back down that painful path, any number of domestic achievements may not save him in 1996.