before i go into this, i have to say that in all the time i spent in europe, i never really considered myself "homeless" since at worst i was pitching a tent in the woods outside of a city, but... everything I experienced there compared to living in the USA, and everything I've heard everyone else say about the two...
the usa is RIDICULOUSLY easy to bum around in. far more than europe. i mean, there's just no comparison. a lot of it has to do with geography. the usa is huge, with vast expanses of open ground between cities, which is a lot different than the geography of europe.
this leads to big differences in architecture, which changes how cities are designed, which changes how people live. it's just 1000 times easier to find some bushes in the middle of an american town/city than it is in places like london and paris. of course, the same holds true for big cities like nyc (hard to find a place to crash, and winter months suck) but most other american cities you can find some place to sleep where you're hidden and won't be hassled by the police.
also, being the "#1 superpower" or whatever, the usa is a HUGE consumerist state and one of the most wasteful countries in the world. the benefit of that for you is that there's a lot of dumpster diving to be had, especially in smaller towns without a lot of compactors.
so yeah, this is a really long answer, but the short version is that if you're planning on visiting the usa and bumming around for a few months, you're not going to have any problems at all. it's so easy it's fucking stupid