Since I really don't think either of the PRC or USA would start lobbing nukes, due to the MAD principle, a conflict between them would just be an exceptionally bloody conventional war.
China's real impediment towards waging an effective war against the US is their lack of a serious and well-equipped navy. Now, they are improving on that part, but it's going to take a while. Whereas, the US has one of the best open-ocean navies in the world, with massive force-projection capabilities, right now.
No navy, no invasion of the US; no invasion of the US, no suppression of the US; no suppression of the US, no way China could win this hypothetical conflict.
Also, keep in mind that the US would have all of NATO on its side, because this wouldn't be simply an issue of terrorist action, like the Iraq and Afghanistan conflicts. This would be an issue of one sovereign state declaring open war on another sovereign state. The NATO countries would be bound by their mutual defence pact to fight together as one alliance. The combined navies of the NATO countries could and would allow them to plant troops on Chinese shores by the end of the first month of war.
Japan would probably not be happy about something like this either. I bet a suddenly belligerent China would make the Diet change their minds about the military, and a "Military Amendment" would be pushed, quickly. The JSDF is already well-armed and well-equipped; all they lack is sufficient size and naval power. Since an ally right next to China would be a valuable asset to the US and its other allies, they would probably let Japan re-arm and start drafting. Once that happens, China would be screwed, facing a multi-national invasion in its south-east and north-east regions; they would be able to hold it back for a long time, but eventually, numbers can only do so much. They are modernizing their army, yes, but western armies are even more modern.
The People's Republic would lose and the People's Government would collapse.