A house with some fairly long term storage foods in the pantry. 50 gallons if water in the water heater. An old 5 foot diameter well in the back yard. Probably 20 gallons of diesel/fuel oil and 40 of gasoline in various tanks. A chainsaw and various trees/stacked up lumber. Generator that can be gotten running in a day or so (round to it problem). Pack of 40 or so AA batteries and a radio that uses them. A couple of 4 wheel drive vehicles.
A local doctor's office and a doctor who lines in the same small town.
Various generators in the town that can power gasoline/diesel pumps.
I think we've got it easily covered for weeks. This town's been snowed in/iced in and without power for over a week a number of times in the past 50 years.
A 2 meter/440 MHz handheld amateur radio.
And that's without making any particular preparations. Give me a few hours and I can at least quadruple the period just by filling up some tanks for fuel.
Of course, that assumes the house and garage haven't been bullseyed/I'm not injured in the storm.
Medicines might get short after a bit, but they aren't short term life threatening things.
Internet or cell phone? Gimme a break.
Waaaaaay down the priority list. Those are almost as low as TV, and I've not bothered to hook up my TV for several years.