Destroing american dreams trough bad spelling:
Lets see:
-The US nukes all the bigger Asian countries (+Russia). Assuming many Russian Missile/Radar operators are drunk so they don't manage to counterattack (allready unlikely). For this first strike to work total surprise is necassary. So it has to be the first major move the americans make (Russia would certainly go to full alert if the US invaded lets say Japan). This has the unfortunate side effect of warning all other countries ("Hey Obama has just changed his first name to Adolf!"). The industrialised ones will try to get nukes/more nukes asap. Every one thats not allready broken or has a very stupid gouverment will mobilise. The US migth still get Canada, Mexico & Saudi Arabia by surprise. But for all other countries they have to attack against well prepared forces. Good Luck
I really doubt, that this nuking would work without a deadbed-counterstrike. There is also the problem of explaining it to the american public. And I remember reading something, that a nuclear war has some unpleasant sideeffects (2 years of winter, fallout,...). Not to mention the economic consequences (no more Nike shoes for America).
But lets asume for a moment, that this plan works.
Now have a closer look on Europe.
According to wikipedia, US Forces in Europe are 96 000. With around 64 000 in Germany and 10 000 each in Italy and the UK.
In Combat forces that seems to be 1 Arm. Division, 1 ACR & lots of support units in Germany and an Airborne Brigade in Italy.
In the other European Countries there are only smaller bases with support & security. In many Countries (as allready mentioned for example in France) there are no bases at all.
What do the European nations have?
Italy has ~ 100 000 troops in the army (with ~200 MBTs), ~ 80 000 trops navy & airforce and 100 000 men paramilitary police.
We can assume that the Italian forces will perform poorly, but still better than any nation the US has fought since Korea.
Germany has a little over 200 000 troops with ~390 MBTs & ~ 280 fighter jets. They are organized into 3 armored/mechanized divisions 1 Airborne divisions & 1 heli division. German Divisions are currently down to 2-3 Brigades, so they are a little weaker than the US ones.
German forces are ~ equal to US forces in training and equipment.
The overall strenght of France & the UK is roughly similar to Germanies.
First conclusion: The US has larger fighting forces only in Germany & Italy.
US Forces in other countries can be dealt with by local police.
Second conclusion: The US forces in Germany and Italy are heavily ountnumberd. They are to weak to destroy these countries armies, but might be able to hold positions against them. (If the use clever tactics and only until these countries build up more forces/reenforcements from other countries arive.)
So what about the "quickly occupy the capitals" strategy?
This could work in countries where economic and politial power is centralized in the capital. The examples for such countries in Europe are France, Portugal, Ireland & Austria. But in none of this countries does the US have forces that could hold the capital even for a few hours.
Germany and Italy on the other hand are among the countries, where economic power is very decentralised. In Germany the same holds true for political power.
Italies industry is based in the North (especially in Turino & Milano) far away from Rome.
The German economy is even more decentral. Even if the US occupy Frankfurt and Berlin, this would not force Germany to surrender. (Would the US surrender if Washington & New York are occupied? And New York is far more important to the US than Frankfurt is to Germany)
//I do honestly belive that the German economy would benefit from the destruction of Berlin.
Third conclusion: The US can not take out a single European country (except maybe Iceland) with the forces it currently has in Europe.
We have also to take into consideration, that US Units moving out to capture key cities would leave their bases vulnerable to counterattacks. The bases were created under the assumption that the host nation is friendly, mainy of the smaller ones willl be quickly isolated and captured.
Fourth conclusion: The US will certainly lose many smaller bases abroad. This will hamper their war effort. US soldiers taken prisoner could also be used as hostages, if the Americans use civilians as "shields".
Airpower: US Airforce Europe has less then 200 fighter jets. This is inferior to the Germans alone.
Supply: Food and gas can be plundered. But where will the forces moving out to capture cities get ammo, spareparts...?
Supply by air would require an almost total air controll, which see above, is
unlikely.
Asia: The situation in Asia is similiar to that in Europe. Including Navy, the US have ~80 000 troops there mostly in Japan, Korea & Taiwan. In each case these forces, even given surprise, are no match for the army of the host nation. (Japan & S-Korea have each 200 000 - 250 000 troops. Some older equipment, but organised & trained to defend their nation in a conventional battle and not for peacekeeping in Wallwallaland.)
Loses: Germany, France, UK, Japan have forces equal or almost equal to the US. Russia, the other Europen Nations, Egypt & Saudi Arabia are worse but still better then Irak.
Firepower and targeting is much better than in WW2. We have not seen real battles between state of the art armies for 50 years. Manovers predict loses of up to 50% of all tanks & troops within a few hours.
Even if the US reenforce Europe & Asia within days their forces there could already be wiped out.
American reeforcements:
OK. Of course the US have more troops than those currently in EU/Asia and will reenforce them.
The Navy (including its air wing) is busy fighting enemy navies, securing transports and hunting Boomers (the submarines not the cylons
).They might even succeed but it will take them some time.
The US airforce is also superior to every other in the world and has the advantage of the first strike. But as explained above it will quickly loose many airbases abroad, as the host nation turns unfriendly. So it has to operate from North America an a few island-bases, while the enemy has his bases right on the battlefield. And this is an enemy that has Patriots, Stingers, Harriers, Mig-29, F-16, Eurofighters and all that
stuff.
Quiet diffrent to Irakies, that train a few hours yearly in their rusty birds.
So don't expect miracles from the airforce.
That leaves ground troops.
I assume the US uses national guard and reserves for Mexico & Canada.
We also substract the forces allready tied down in Europe & Asia.
That leaves 4 Mechanised Divisions, 4 Light Infantery/Airborne Divisions, 2 1/2 Marine Divisons & Change.
Note, that some of this troops are currently fighting/recovering from fighting the War on Terror. That means:
1) they have combat expirience (good)
2) are tired/not ready for depolyment elsewhere (bad)
3) focussed on anti-guerilla operations and not on conventional war (baaad)
Just for comparison: The invasion of Iraq required 4 American & 1 British Division + change (all in all ~300 000 troops, not counting Iraqi opposition).
So what can the US do with this force?
1) Split it and send 3 Divisons each to Asia, Europe & the Middle East.
Most likely result: Draw in the ME, US Forces in Europe & Asia whiped out.
(see above for opposition & likly caussalities)
2) Focus on where they can win (& wining brings benefits)
Most likely result: Pyrrhic victory on one (max. two) theater/s, but the others have time to arm. US now allready overstretched and faceing fullscale guerilla wars in several countries, while at least two major enemies are still around (and not idle).
Note that in both cases Africa & South America are still free.