"I'm not sure I could do it."
Well, of course it is possible. The question is whether that is what you want to do. In the military battlefield, Long Range Patrols go out for days with no more than that. Just think of GI Jane from Santa Barbara.
A trip like that would be likely in Death Valley by picking the right season and the right elevation in order to hit the weather that you desire. Instead of a proper hut, you can find your way to an abandoned miner's cabin. Or, in another part of the park, there are miner's dugouts (like caves). The park service has a dim view of visitors actually staying in them, but they would have to catch you.