Acctually, when I was younger and had no life at all, I developed a strategy for how an army of about 50 million could successfully invade the US. Granted, that's a very large army, so you would need China, India or an international cooalition... and you would also need the cooperation of either Canada or Mexico, but preferably both. You couldn't take the whole thing, but you would be able to force us into submission. Not that hard really.
In a side note, the only three countries I determine probably could not be successfully invaded were... suprise, India, China and Russia.
Even if you had a 50 million man army and had allies that bordered India, China or Russia? I'd argue that it would be MUCH easier to invade and control any of those 3 over America. The populations of those countries are used to being controlled by force, in fact, it almost seems like Russians crave
being put under the boot of an evil leader. Americans on the other hand tend to be pretty spoiled on Freedom and Liberty, so much so that we take them for granted. Take those away from us and we'll make the Iraqi insurgency look like child's play. Plus, it would be much eaiser to get the Ukraine, Latvia and Finland to play along with an invasion of Russia than it would be to get Canada and Mexico to play along with an invasion of the US.