I went last month on the same trip, my first time in China, using the exact breakdown of days. It is really sufficient.

I used the good advice of the board posters and avoided the tour groups, travelling by public transportation and with a good guide book.

It is very doable and I feel that I got to see a part of the big cities that no tour group would show you.

Do it by yourself. With the internet it is easy and much more fun.

P.S. Just a note of paranoia. After each reservation on the internet, hotel, flights etc. I called the airline and hotel in China to make sure they had the reservation. They all did