Pretty much everything was said really.
It is, theoretically, possible to assault and conquer parts of United States with military force.
But "first strike" and prevention forces U.S has notwithstanding, the route between the U.S and say, China or Korea is pretty long. Sufficiently long so that carrier battle groups or subs would beat the crap out of approaching fleet, or at very least deal pretty heavy damage to it. Then your army would have to actually make it to the coast, and break through the eventual American defensive lines - who would hit you with everything they got. Tanks, missiles, airplanes, naval units, commando team, electronic warfare, internet warfare etc. Then, you'd need to push further into country.
Since I doubt U.S citizens would roll over (not to mention any partisan-style special forces teams or broken-up military units that would be stranded/left behind the front-lines,) you'd need a sizable force to just maintain order, much less keep the momentum of the offensive. I doubt that more then a few nations would have the manpower to do it - I mean China and India of course. Alternatively, you would need a pretty big multi-national alliance.
And one thing a lot of "armchair", for the lack of better term, strategists forget that military losses cannot be as easily replaced as in an RTS. Soldiers, tank crews, pilots, all of them take time to train and equip. And no nation has an endless population - you need people in factories, on farms, to make more children too. Chances are your entire military will get floored trying to invade U.S - and before you come even close to replenishing losses, Americans will bomb the shit out of you, and everyone you ever loved, and you won't be able to do anything about it.
Even assuming you could somehow to land with minimal casualties, you'd still need to supply your army. As many people here said, the sheer logistics of moving a mass of people across oceans is mind-boggling, even without other people trying to sink your fleet. Overlord was nearly a failure because of logistical trouble, and it "merely" involved shuffling Allied troops through La Manche channel to France - a distance that's several dozen kilometers long at most. The distance between Korea and North America is measured in millions by comparison.
And remember, at all times do Americans have the capacity to carpet-bomb your homeland at any time of the day, courtesy of carrier groups and military bases placed all around the world, many of them in Asia.
In short, it's possible, but entirely pointless and a waste of time.
Of course, if you had troops stationed beforehand on American continent, and even better, kept it secret from Americans, your chances would be much better. An army that operates from Mexico or Canada would fare better then someone who needs to haul their ass across a vast ocean. But keeping your military build-up is no-easy task, and has it's own set of problems.
And there's the whole global alliances thing and nuclear deterrents.
Of course, things get a bit different when you attack separate American bases far from home, rather then just invade their homeland is an entirely different matter.
After all, why bother conquering a big piece of unfriendly land, if you can defeat their military, achieve global supremacy and confine Americans to their borders? After a few years, they'll be begging for peace, as you slowly blockade them into oblivion.
...Assuming you *can* beat them. American army IMO has some of the most advanced armaments and is by no means a small force.
Just throwing in some of my few thoughts with two cents into the mix.