can I get an entry visa when I land

The one on arrival is impossible for US citizen unless you have very urgent thing to enter China. Usually, you need to have an invitation letter for applying it.
For your situation, it is almost impossible to get it.

Personally speaking, if you do not want to affect your trip seriously, you are suggested to go HK for a stop, where you can try to apply for an ordinary Tourist L. I heard some local tour agency can help travelers to get it in a short time, maybe around one to two days. The service fee may be a little bit high.