Yamaha 2400ishc starts/runs my 13.5K btu A/C unit. For extra assurance, and to take some of the strain off the generator during A/C start-up, you can add a $15 start capacitor (goes in parallel with the A/C's run capacitor).
I opted for the Yahama 2400 versus two Honda 2000's because I didn't want to pay the extra $500 for the Hondas and didn't want to lug around two generators. In addition the Yamaha is relatively light (70 lbs) versus over a hundred pounds for a single 3,000 watt generator.