"Do you have any idea how big of a generator you're going to need?"
That depends on how leaky your building fabric is.
I'm not in NY, but max heat demand for our house (retrofitted 1920s brick constructions with a family of 4) is 2 kW (-5C outside, 21C inside).
I know NY gets colder, but it should also be pretty easy to get better building fabric performance for a new build (which is what we're talking about here) than I get for our 1920s house.
Let's be pessimistic and say I heat it with a heat pump which only achieves a CoP of 2.0 under those conditions. Let's also ignore incidental thermal gains (100 watts per waking human).
Total electrical power to run the heat pump would be 1 kW.
Doesn't sound like a monster gen-set to me.
Don't want to maintain a genny? I could run that (vehicle to load) from an electric car battery for 3 days. If I drop the set point temperature, reduce the ventilation rate and decide to stop heating the lowest floor, I could stretch that to over a week.
That's assuming no other significant loads, but also assuming no generation from the 4kWp solar PV I have on site (if you're not fitting PV to a new build, then that seems nuts).