Buy a Coleman Polar Cub AC and your Honda EU2000 will run it just fine. If you are one of those lucky guys who owns a camper with 3 rooms and a wine cellar, you may find that the Polar Cub does not meet your needs, but for the rest of us, it works pretty well.
PS - has anybody tried the anti-theft adapter that Honda is marketing. Kind of a metal overplate for the plastic handle of the generator to keep creeps from cutting the handle to steal a generator locked by a cable? Camping World has them and they look pretty slick.
Happy Camping!