We have a Yamaha 3000 watt inverter generator, rated at 2800 watt continuous, similar to the Honda 3000 watt unit. We run a standard Coleman 13,500 AC roof unit with the generator. On a hot day, when the starting load on the compressor is highest, the generator will start the AC, but it sound as though there is little reserve there during the 1 second it takes to start. As a rule of thumb, the starting amps for an AC compressor, which starts under load, is between 8 and 10 times the running amps. If running amps of the compressor only is 11, then the instantaneous starting current could be as high as 88 amps. This is what the generator must contend with.

I haven't tried running AC with a 2000 watt generator, but I have heard that it is very borderline. It works for some people and not others. Best to stick with a 3000 watt unit, or two 2000 watt units with a parallel cable, available form Honda.