Not so much. I have calculated that three weeks of travel would cost around €4000 per person, probably less. Flights are the most expensive part, around €1000.

It's easy to make plans in Herz website. For example Ford Explorer for 3-weeks would cost $2735. Ofcourse it is a lot cheaper to divide driving costs with several persons...

https://www.hertz.com/rentacar/reservation/gaq/index.jsp?targetPage=whatView.jsp

Staying in small hotels only costs $50. Fuel is still quite cheap by European standards. Also dollar is very cheap right now. Clothes and shoes and electronics are very cheap...

Here is a interesting website which tells about the different routes you cantake accross the US:

http://www.roadtripusa.com/

Ofcourse it would be nice to visit ghost towns in Oregon, Montana etc. if easily reachable.