You can, but it's expensive. Even my little 5500W uses a half gallon an hour with no load. A battery bank, an inverter, maybe some PV panels, and a generator on-demand might get you close, but I'm thinking the infrastructure costs would still be pretty substantial. The grid has the benefit of being able to average loads over the entire system and ramp production up and down as demand requires. That's tough to manage when it's just one house.
There are people living "off the grid", and they seem to do fine, but when you get down into the nitty gritty, they've given up a lot of convenience in order to live that way.
