I've run my AC/Heat Pump occasionally on 20 amp service. According to my power monitor system, the startup current draw is 17-18 amps, so make sure everything else is off or you will quickly exceed 20 amps. If the weather is warm enough for a heat pump to work, then the furnace would likely not need to run much to keep things warm. I would just use that and save the 20 amps for coffee pot, microwave, battery charging/12 volt convertor, etc.
2012 Forest River Sunseeker 2300 Chevy