In answer to this fascinating and highly imaginative thread, I would like to turn the question on its head.
(Actually, given GWB’s eccentricities, it seems less hypothetical than the other one.)
OK. Let’s say some US President (Bush) just gets fed up with the rest of the world one day: “World, I’m tired of you. I’m tired of you not doing what I want and giving me everything I want. I’m tired of your endless doubts and discussions and funny-tasting cuisine and funny-sounding languages. THAT ENDS TODAY. No more countries, no more diplomacy, no more international affairs. One planet, one government, one President. It’s all US now. Let the invasion begin!”
(DC Comics fans: remember when Etrigan the Demon ran for President in '92, and his campaign showed him throttling an anthropomorphized world globe?)
Some of the advantages and disadvantages discussed in the other thread would also be at work here. Disadvantages: the rest of the world has some pretty formidable geography (mountain ranges, oceans, deserts, very long distances). Also, there would be a lot of partisan resistance, rogue remnants of conquered armies, suicide bombers, etc. It would also be very, very expensive, but that could be partially offset by all the resources we would capture. Advantages: most of the rest of the world is too plagued by poverty, inefficiency and lack of technology to oppose us, although it must be remembered that the world also has some wealthy, well-armed and technologically advanced countries. Whaddya think, take out those countries first?
(In case your brain is in shock from the audacious unlikelihood of this scenario, try another scenario: could the US successfully invade or hold Russia, China, or Europe? But please, make a crack at my original scenario before copping out.)