I don't know about the US, but I spent 3 months cycling around Australia, two years ago, and spent approx. $30 per day.
During that trip, I stayed in hostels about once or twice a week, I stayed with friends quite a few nights, I camped in real campgrounds most of the time, and I stealth camped several times.
That $30 per day included my accommodations (if I had to pay for them), my food, my alternate transportaion (I rented a car for 3 days, took the bus 3 times, and took city trains a few times), some repairs (including a $75 hub replacement), and sight-seeing (like a cruise out to the Great Barrier Reef to name one of several similar sorts of things).
However, I would guess, based on my very recent travels through the US, that $30 per day might not be adequate.
Campgrounds in the eastern US in particular were surprisingly expensive ... a whopping $30/site for a plain, ordinary tent site in one rather run-down commercial facility, and the campground guides I have indicate that there were several others much more expensive. The State campgrounds were better value for the money, but were still around $20/site. They did seem to be less expensive in the middle of the prairies though.
Australian campgrounds were fairly inexpensive in general, but if you rode anywhere near the main roads, they had rest areas. In the US, the rest areas are great for short stops (picnics, toilets, etc.) but you can't stay overnight in them. In Australia, the rest areas allowed you to camp for free for up to 48 hours. And in remote areas, stealth camping was easy.
As for hostels, Australia had hostels in pretty much every town I went to ... and most were very nice - well-kept, clean, quiet, etc., and they ran for about $20/person. However, in the US, there aren't very many hostels, and the quality can vary widely.
And hotels/motels can get expensive. I found I was paying approx. $60-70 per night in all the locations across the US where I opted to use a hotel. The grottiest and the cheapest of all of them was about $60 in a small dot-on-the-map town in Montana.
As for food ... if you acquire all your food from restaurants, your cost will be much higher. However, if you buy your food from grocery stores, and opt for store brands, etc., and cook your own food, your food costs can be fairly low.
In Australia, I ate at a restaurant probably about once a day for about 30 of the 90 days I was there. Fortunately, I discovered Australian hamburgers. For about $8.00 I could get enough french fries (wrapped in a newspaper) to feed an army, and the Australian hamburger, which was a complete meal in itself!! Each hamburger consisted of: bun, usually two large patties of meat, cheese, a fried egg, a thick slice of beet, a thick slice of pineapple, lettuce, a thick slice of tomato, pickles, and a bun to top it all off. I can to take it apart to eat it!! MMMMMMMmmmmm!!!
One of those a day, and I was good to go for the whole day! But, unfortunately, we can't get those sorts of things here in North America, so we have to buy food from a grocery store to save money.
So basically what it boils down to is this ... if I were planning a trip across North America, I'd aim to have somewhere around $50 per day available to me. If you don't need it, that's OK, but if you do need it, it's there.
Incidentally ... I'm not sure what you are referring to when you say "hamiltons" ... I'm guessing money?? But when I first read your title, I thought you might be asking how many Hamiltons (towns, cities, villages, etc.) there are in the world. That might be an interesting tour ... cycle to all the Hamiltons in the world!!
I can think of several, in several different countries.