There are parts of the U.S. where housing is pretty cheap, down to about $100/room/month, probably less if I searched further. Assume that people are packed in ten beds to a room, along the lines of housing for tramps in London as described by Orwell in Down and Out in London and Paris. That gets annual housing cost per person down to about a hundred dollars.
On further thought, that’s too high. There are parts of the U.S. where the weather is temperate enough so that living outdoors, perhaps with a roof to shelter you from the rain, is not a serious risk to health. So all you need is some empty land in such an area, enough roofs for everyone to huddle under when it rains, and local authorities willing to put up with the land being used as a refuge for the homeless. Cost per person close to zero. Add a little for porta-potties and a water supply.
I should probably include clothing. [...]
Adding it all up, it looks as though a serious estimate of the cost of “basic needs” in the U.S. at present, taking the term seriously as describing what it takes to stay alive, would come to something around $500/year.