From the Honda Page...
http://powerequipment.honda.com/generators/generator-how-much-power#Starting
We are aware the NEW Honda models about 3 yers ago were down graded in the amperage department.....13 amps is the limit now...and we are talking the 2000 model....
That 13 amp draw is real close to the limit...
AC Output 120V 2000W max. (16.7A) 1600W rated (13.3A)
Honda recommends to use only 80% of rated value or the 1600W the user manual states not to use the full 2000W for extended periods of time.
to quote....
My appliance is a 1000 watt model, but it takes 1600 watts to run it. Why?
Some devices are labeled or promoted with a power number. For example, a hair dryer might say "1000W." This means the hair dryer itself produces 1000 watts of heat energy. But the amount the hair dryer uses from a power outlet is always more than it produces in heat. This is because the device’s energy use is not 100% efficient.
Another example is a microwave oven. It may be marketed as "1100 watt oven" and indeed produce 1100 watts of cooking power, but it will require more than that from a generator.