If China manages to do this, then we will have people on Mars in under 2 years. Competition from china is the only thing I can see spurring the USA into action.
Far from. It takes nearly 2 years just to get to Mars. Also, China tends to be a fast copier , not a leader. They seem to leave the bulk of development costs to someone else. So I think it's unlikely that they will front the resources it'll take to make a Mars mission possible.
Wasn't there a famous Chinese guy who said something like "never underestimate your adversary".
In the past that might have been true, but things change. Just one example A lot of people have been educated in the US, and are going back to china to start companies.