In the end lodging and food will be over 80% of your costs. If you can do more camping and cook your own food you can be below $30 although campgrounds can get expensive. you can make a pretty easy meal out of pasta or 10 minute rice, a can/packet of tuna and a can of vegetables (or better yet dehydrated) with a few seasonings mixed in. This was a staple of my diet for months when I hiked the PCT. Also there isn't a big hostel network in the US but it does exist particularly along the AT and PCT. Not sure where you would go to find this information though. warmshowers is another good site if you want to lower your costs.

I did a 9 day tour in Taiwan where I might have broke $10 (certainly <15) where I camped at police stations and various other spots. This was going a little too cheap though.