The ChiComs cannot project that military force. They have a huge land army, but a laughable navy and air force.
The ChiComs aren’t stupid to resort to nukes.
How do you know they wouldn’t use nukes? They’ve hacked enough of the US military systems, so it may be that a counterattack would be hobbled by them. Very few US generals/admirals would think to take matters into their own hands too (in spite of Sun Tzu’s advice to do so when appropriate), given Obama’s reorganization of the top brass.
And why does it seem to me that you presume that Obama has the nerve to take them on?