It's not a completely silly question but you may conclude that this
isn't the best approach either.
The gadget that converts 12-ish V d.c. into 120V a.c. is called a
"power inverter." Punching that term into your favorite search engine
should yield plenty of websites about them. People use 'em to run
*small* 120V appliances in their car or sailboat or wherever. Doing
this is pretty inefficient, so the inverter sucks a lot of input
current and gets nice and hot.
Small ones (few hundred watts steady-state, a bit more than that peak)
are ubiquitously available for as little as $30, but those are best
thought of as a way to let the kids play video games in the back seat,
or perhaps for you to run handheld power tools at a jobsite.
Bigger ones can provide as much as a few kW steady state, but we're
now talking about prices that start well into three figures and run
into the four-digit range, especially if you want gourmet 120V
comparable to what the power company delivers, rather than "close
enough for government work" stuff.
The big ones also drain a battery in a big hurry, and are really
happier with a jumper-cable-style or (robustly) hardwired connection
than with the cigarette lighter outlet. The usual recommendation is
that you keep your car running while using them and/or employ a
separate, deep-cycle (marine-type) battery.
Your proposed application would need one of the huskier ones -- a
residential furnace often has a surprisingly substantial motor, 3/4 or
even 1 hp; and motors usually aren't too happy with either
undervoltage or trashy waveforms. Some advise allowing as much as 3x
the steady-state current draw at startup, so check the peak as well as
the steady-state specs of the inverter.
You might well decide that either there's a cheaper way to get AC in a
power outage or there's a better emergency way to keep the place
PS. Also, educate yourself on how to properly hook up and use a
generator or other alternative AC source so you don't throw it into
the teeth of an overload... or (eeek!) energize a line that somebody
assumed to be dead. (Yeah, we all know what they say about "assume,"
but accidents happen somehow...)