The American Discovery Trail proves that this is possible, but bear in mind that most of that trail is road walking. I read Lion King's journal of his trip on the ADT a few years ago, and, frankly, while he seemed to have enjoyed most of it, it did not sound like fun to me! It would be even worse farther south. To the best of my knowledge, until you get at least to west Texas, there isn't much public land across the southern tier of states. The expense of buying right-of-way over private land would be prohibitive. With the Grand Enchantment Trail, half of Arizona and New Mexico are already covered. The western part (into California) and the eastern section (Alabama-Texas) would be the big issues. Andrew Skurka proved that the western section can be done; it's the eastern 2/3 that is going to be the problem.