I have really low gears on both my road bikes (11-34, and 11-36), and it's great for climbing (we have a few hills here in Colorado) but they are both triple chainring bikes. You may be able to put a bigger cassette on the back of your compact crank bike, but it might depend on what your components are.

If you want a bike to ride the southern tier with how about something like this? It would be good for carrying small panniers with your clothes, etc. It has a triple in front and 11-32 in the back. For $600 is a good deal.
http://www.bikesdirect.com/products/windsor/tourist.htm