The refrigerator seems like the only real substantial load. I looked that up, and while it'll draw over 1kW when starting, the continuous load is something like 200W for a modern one. Nothing else is in my house is going to approach that. I'm not going to be running desktop computers during an extended outage, and laptops will add a negligible impact. In colder weather I'd want enough power to run the gas furnace, which I imagine is not a ton. Lights can be kept to a reasonable minimum, and you'd want LED bulbs available for all the lights you'd use during an extended outage anyway, and so also won't be a whole lot. Thus: a few hundred watts.

But let's say you need 2kW. (That's not quite double what a normal car can put out, from my quick research. Typical car systems seem to top out around 1200W, give or take.) The Tesla would be able to provide that no problem, of course, but! It'll only do so for about 22 hours before you run the battery all the way down, at which point you have no electricity and no transportation and no way to remedy either until the power comes back on. If you really do need 4kW then your Tesla will last you half a day, which is just about useless. If your needs are low enough that the Tesla battery could last for a couple of days, then you can run off a regular car too.