Warning: Academic-type stuff here. Lengthy stuff.
The Chinese government could (bigger army, though with less high-end weaponry)
Not so much with this one.
(Finally, all those years of grad school pay off!!)
Least not at the moment. Because while, yes, on paper they have the world's largest army, they lack projection power. They don't have the resources to go any where fast enough that isn't in their immediate vicinity. It was only somewhat recently, for example, that they began having anything that resembled a respectable deep water navy. They could patrol the heck out of their coast, or invade Taiwan[SUP]*[/SUP], but they lack the ability to get their massive forces much further than that.
Starting a land war in Asia would be a really bad idea - Vizzini was right on that -but in terms of invading the US, it's just about as likely as Soviet troops parachuting into Montana during the Cold War.[SUP]**[/SUP]
Possibly even less so.
Part of this is cultural - the Chinese only really had one time in their history when they looked much beyond their own landmass in terms of exploration. (Which is a shame, because the Chinese era of exploration was awesome.) They never really had to. People came to them with things, and if they didn't, they weren't interested. Then, they were occupied during the Colonial Era when everyone was out empire-building, and by the time that collapsed pretty much around the end of WWII, the Chinese had to finish off that pesky civil war they'd been dealing with since before the Japanese showed up.
Add to that several very inward-looking movements that closed China off (including the Cultural Revolution), and there hasn't been the impetus to have the ability to project their military power. Again, they haven't really needed to, either, although this is not to say their current military isn't aware of this lack.
Fundamentally though, it would be
nigh impossible exceedingly foolhardy for the US and China to go to war. I'm not saying it couldn't happen, but the resultant embargo on both sides would cripple both economies. They need us just as much as we need them.
Which is a good thing, really, because even without their ability to project, if they wanted to throw their military weight around in Asia it could get really scary, really fast.
[SUP]*[/SUP]And *that* is a nightmare scenario for a number of reasons, not least of which is US defense pacts and any number of Chinese generals who would actually do it, much like there were both US and Soviet generals who would have gone through with nuclear war.
[SUP]**[/SUP]With apologies to fans of Red Dawn. But while the movie was great fun, it was premised on the most ridiculous of premises. Like the Rocky IV of premises.
You should know better by now...