A Honda eu2000i will probably start and run your 10,000 BTU Air Conditioner, unless itís an older unit. Iíve read that the eu2000i wonít start a 13,500 BTU Air Conditioner, so I thought Iíd give it a try on our 2016 Flagstaff Micro Lite 21FBRS.
Conditions (Wanted to give it a fighting chance):
2014 Honda eu2000i Generator (NOT on ECO Mode)
Fuel: TRUFUEL (Expensive, but no fuel gum-up)
1300 ft altitude
95 F Ambient Temp
Air Conditioner had been off for 15 minutes.
Shut all AC Breakers off except the Air Conditioner.
Started Air Conditioner Fan on LOW first, then started Air Conditioner.
The Air Conditioner started right up. I then put fan on HIGH and turned on other breakers (Refrig and Water Heater on gas, didnít try on AC).
The Honda isnít the cheapest, but it seems to have more reserve starting power than most other comparable size generators. If you can borrow an eu2000i, it might be worth the time to try it before buying two generators.