Honda 2000

Any engine under a strain won't last very long. Why ruin a good generator by overloading it constantly, get one large enough to do the job.

Agreed, but the question is about an 11,00 btuh air conditioner. Every one is different and you don't know what the power consumption is without measuring it. I can offer as an example that my former Dometic Brisk Air 13,500 unit pulled 1,400 VA from the eu2000i, or 88% of its rated continuous load. The engine did not run at its maximum 5,000 rpm. After a few seconds of startup, it didn't even rise off of its eco off floor of 4,300 rpm. A simple interpolation, which may or may not be valid, would have the OP's air conditioner pulling 74% of the eu2000i's rated continuous load.