To start with, I think it is only fair to consider the bike itself as a cost of the trip if it would not otherwise have been purchased. But, the neat thing is that a bike which is suitable for touring is also ideal for commuting by bicycle. As such I already had the bike and almost all the other equipment needed for the trip (with the exception of the camping gear), and expect that the bike will more than pay for itself in savings on fuel, repairs, and parking as I use it to commute to and from law school over the next three years.
In two areas - food and entertainment - I think most people would actually spend less on this kind of bike trip than they would spend if they stayed at home. Obviously, passing through towns as small as most of these are, there's really nothing to spend an entertainment budget on. As regards food, there's nothing stopping you from using grocery stores just as you would at home, but more to the point I strongly suspect the average person would spend less on restaurants while touring than they would at home: what you find are a lot of small restaurants that offer excellent quality at prices only slightly higher than fast food. For example, I've had some of the best Mexican dinners I've had in my life for $10 (which included a generous tip).
I'm planning on replacing the bicycle's chain every thousand miles, since replacing it before it starts noticeably stretching greatly extends the life of the bike's gears. Chain replacement costs about $40 for chain+labor if you let the bike shop do it, which I generally do. I'll probably also have to replace the rear tire a few times, and the front tire perhaps once, during the course of my planned trip. The tires I use run to about $35 each if I remember correctly. In all likelihood, these will be the only bike-related expenses I'll have for the remainder of the trip.
So, that leaves housing. Of course you can just camp most of the time, which is free. A step up from that is camping at RV parks, which around here seems to go for $7-$10, and depending on the RV park shower or laundry facilities may be available. And of course the other option is budget hotels/motels, which you'd probably need to do every once in a while. The place I'm in now is $26.95/night, though obviously deals like that would be harder to find in San Diego (for example). I suppose I should admit that I personally prefer the inexpensive spots, just because they're more likely to have some quirk that will make my stay there more memorable, i.e. for one of the same reasons I like using hostels when they're an option.
So, that's the rundown on the costs of bicycle touring: as you can see, it's a very affordable hobby.
You also don't have to be in great shape, as long as you have patience, are willing to accept lower mileage and more rest days at the beginning of your trip, and get an early enough start on days including mountain passes so that even if you have to walk the bike most of the way up you still make it down before nightfall.
In short, I think for most people not yet in retirement, the main obstacle to doing something like what I'm doing now would be time, rather than cost or physical fitness.