Well, based on the evidence I'd imagine China got hit back even harder.
Generally speaking the simple fact that DC isn't a crater shows that we did pretty well defensively, wiped out all the opposition before they could fire more than one volley, or perhaps both.
However, China did have people on the ground in the US, though they seem to have been infiltrators disguised as factory workers and such rather than an actual invading military.
The way it seems is that there was enough left of the US military to form TWO seperate factions. The Brotherhood Of Steel, and The Enclave. Some information on the computer terminals in the Pentagon (in Fallout 3) sort of points out that the beginnings of the BoS were military renegades that had some kind of conflict with the scientists they were working with, though the actual details of what those scientists were doing is sketchy. Both the BoS and Enclave being so powerful and numerous that neither can exactly laugh the other off, despite The Enclave having better technology.
Operation Anchorage might very well answer some of the questions we're discussing.
>>>----Therumancer--->