In reply to neil9216:
Just to avoid any confusion - that stretch would only take a couple of days (if taken at a leisurely pace), so I assume you're only really asking about one or two nights of accommodation? If you're talking about the full two weeks, then you really need to get out the maps and guidebooks and have a rethink - you could have a much more interesting holiday with the same kind of cost/time.
The advice above about wild camping is correct. In the USA, it's generally a good idea to plan your journey and figure out which state parks of NFS campgrounds to use. It's often worth the spend too - campgrounds are often very good.
If you've two weeks, consider coming in to Salt Lake City and then looping out east to take in Utah's parks before heading over to LA. You would have more than enough time and it would be a dramatically more worthwhile trip IMHO.
As a general rule, you'll need to think about booking ahead until around October. In peak season you can squeeze into forest and state camps if you get away from the most obvious ones, but will be taking your chances in the bigger parks or near major highways and towns. Out of season you've much more flexibility. For that part of the world an autumn trip is actually a good plan as it will be much cooler.
There's so much amazing scenery out there; don't spend a fortnight looking at scrub and dodging bullets...
Mark