a furnace takes roughly 4 amps x 120 volts = 480 watts. the problem is unless you get a high quality generator with an electronic governor/speed control the frequency of the power will vary from 58 to 62 hz and that can damage the circuit board. there are whole home generators that have that but your basic Honda portable one does not. they are designed for power tools. the power needs to be a steady 60 hz. I have a expensive electronic power conditioner that I bought from an electronics store for around $300 to use with my Coleman generator. Not the same as what you buy for a stereo (Monster) from a stereo shop either.
"Cut it twice and it is still too short".