Another possibility is your AC!
If you have a high-quality generator (like a Honda), and your AC is NOT bigger than 15K, it can probably run your AC too. You might want to check out the "Micro-Air Easy Start Install" thread (about the 30th thread in this forum). That thread is about a device that makes it easier for generators to start the AC and enables more generators to do it and at more extreme conditions (elevation and temps). You would need to balance your load (e.g. unplug stuff) to avoid overloads, but it can definitely be done. Good luck.