Most posters are giving their opinions based on RV A/Cs. The OP has a portable A/C. My first Eu 2000 was purchased to run the small window unit that our new Casita TT came with. I think it was on the order of 11K BTU. The Eu2000 would bog down (eco mode off) when the unit would first turn on and go into overload. There was no problem when running it off line ac power.
This same generator has no problem with our Coleman 13.5K BTU RV A/C on our current RV.
I suspect the surge current on some non RV units may be higher.
Dick