I can see that, but that would probably be a containment issue rather than an actual clash of forces. We could conceivably (note that I am not necessarily recommending this course) use tactical nukes to erase their army without needing to get down and push them out. It might not even be us. Japan would almost certainly get embroiled in this, and they would have to rely almost entirely on technology for their response.
My guess is, just as with WWII, there would be significant ground fighting...major ground fioghting...if it ever got going in a big way, ie. WWIII. I believe every Islamic Fundamental regime, those regimes in S. America cozing up to the Chinese, and who knows whom else would jump in on one side or the other.
Not a pretty picturte at all...but sadly, unless we pull a Reagan style, in your face, challenege very soon that backs these people down...I am afraid it is shaping up that way, and pray most earnestly that I am wrong.
Keep in mind that China has threatened to nuke us too. And more or likely on a shorter fuse. And GWB retired ALL of the MX missiles, and half our B-1Bs. And drastically minimized the protective dispersal of same...and still has Project LookingGlass sitting on the ground moribund. And has four Tridents being converted from a serious strategic weapon into tactical weapons, with cruise missiles.