We're 34' and had no problem from that standpoint. It looked to me like most all of the sites would accomodate big rigs easily, with the only certain exception being the water front sites which are primarily geared for tent, van, class b or small (24'?) class c's.
A 31 foot Class C can fit depending on the site. If you go to the reservation system for Arizona State Parks you can select the sites that are available and check out their site length to see if you will fit. They do have a number of big rig sites but they may not be available when you want to visit. Good Luck!