No. The heat pump (your outdoor unit) and indoor blower motor will run ok at these power levels, but here is the bad news - if the heat pump can't meet the temperature demand (or it gets below ~ 20F outside), the furnace will attempt to turn on several electric strip heaters (as emergency backup). These strip heaters are rated from ~ 5000W to 20000W, depending on the size of your home. Your generator can't handle that load.
Before you follow any of these instructions, make certain that you check with the documetation that came with the generator, since I can't be certain of what your generator is doing. The following assumes that the generator provides 220 output and is NOT 3 phase. If it's 3 phase, all of the following is wrong and don't do this! In general, 220 circuits have 2 110 "leg's" which are nothing more than a center-tap into the 220 source. It can be a center tap on a transformer or a generator. The center tap is designated with a white wire, and the two "hot" lines are usually designated with either black or red. In the case of your generator, if it is not a 3 phase circuit, the 4th wire is probably green which is the universal indicator for a ground wire. To be safe, it is a good idea to ground the generator using a long, copper grounding rod that has been driven into the ground and using a good sized wire (typically #10 or larger) connect it to the generator at the grounding lug, again, see instructions that came with the generator. To make the welder work with the generator, you can "get by" connecting the white wire to the white of the generator or if you're using a plug connect it to the silver screw. The two black wires or the black and red wires are connected to the two brass colored screws. Whenever a ground wire is provided on a wire it should be connected to grounding screw of the plug. I hope this is enough information. If you have any questions, contact the manufacturer or a local electrician.
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