[Instar]

A couple problems Ive seen:
About the US military being capable to take on the entire world, yes it is a bit of a stretch, but consider, the US Navy and Airforce are completely unmatched. A single battle group consisting of a carrier and support vessels usually has more attack aircraft than most nations. The US has 12 full battle Groups, of which usually 2-3 are in major overhaul, around 6 are in port, and about 3 to 4 are at sea. If serious effort was put into putting all out to sea, I bet a max of like 6 could be reached feasibly. Britain's carrier fleet, although impressive in its own fashion, pales in comparison. The British carriers are much smaller, and operate only V/STOL aircraft. No other Navy comes close (the Russian surface Navy is generally a joke, their carriers are the same idea as the British, I believe; similarly, I don't think the French carrier is seaworthy yet). The US Submarine fleets are the same, for the most part. The Ohio class is generally undetectable, and the Los Angelas class is a very potent boat. The Sea Wolf class (as I recall it being named) is only limited to about 3 or 4 boats I think, so its numbers are almost inconsequential.
So the US Navy probably could destroy most all other Navies and stop a lot of the world's shipping.
Problems with this is that the US lacks sufficient ground forces to invade and garrison large regions of the world. China has insanely huge masses of infantry, but they are for the most part undertrained and underequipped, but that may be changing. The problem for the US would not be taking the ground, but keeping it. As it is, US Armor and Armored Cavalry are for the most part unstoppable juggernauts, if used correctly. Armor though, cannot be effectively tasked to garrison regions.
As to nuclear weapons policy:
In the bad old days of the USSR breathing down Europe's back, the US (and NATO) were of the position that the Soviets had so many tanks and other armored vehicles as to be impossible to stop, as NATO tanks were vastly outnumbered (the US could not feasibly deploy enough tanks to Germany to counter such a threat). To counter this, the policy was developed that NATO would employ tactical nuclear weapons (not strategic nuclear weapons) to destroy the Soviet blitz. (A great deal of emphasis for NATO in preventing USSR from invading all of Europe involved the Fulda Gap, I believe, and the Fulda Gap is one of the most popular scenarios in tank sims, like ATF or BCT, I think) This kept the USSR from attacking.
By the way, nuclear weapons can be subdivided in a couple different ways -- tactical and strategic. Tactical weapons are supposedly for use on a battlefield, and generally range from 100 kilotons to just less than a megaton in yield. Strategic nuclear weapons are used to obliterate cities, and range from 1 megaton to 10 or more megatons. (However, I think that the US doesn't employ many weapons that are close to 10 megatons.)
One Last thing: The US probably has plans for delivering nukes onto EVERY country in the world, even allies. Its paranoia, but dont take it personally.