Actually, the natural gas generators for residential homes run about 4K-6K w/ auto switch (installation included). So they really aren’t that far fetched.
I currently have a borrowed Yamaha 6600DE generator that was more than adequate to run my sump, furnace, 2 de-humidifiers, lights, and my TV/ PS2/Xbox without a hitch. I erred on the side of caution, and usually once the house was heated, I shut off the breaker to the furnace, the same for anything else. The only thing that was always on was the sump.
Ironically, 4 days before the storm, I ordered a 4500 generator. Irony at it’s best. I since cancelled the order after using my buddy’s Yamaha and I plan on buying a similar 6000 or more generator. In two years or so, I will probably get a natural gas generator.