My Honda EU2000i ran for 36hrs continuously since the blizzard. It was tied to the main electrical panel, backfeeding through a 220v breaker, with a jumper to carry the juice to both legs of the panel. Main breaker is OFF for this kind of thing. I fully understand the liability of such a setup, the danger of backfeeding the lines, killing a linesman, etc. Please spare me the lecture on this, I lock out the main breaker before I setup the generator, there is no danger to the public.
That said, the EU2000i powered the entire house, all the 110loads. That included: gas furnace, pellet stove, fridge, tv, cable, lights, etc. Yes, it will not run a coffeemaker, microwave, dishwasher, toaster, hairdryer added on top of the basic house loads but who cares? I had heat, food, lights and entertainment throughout the blackout. Many of my neighbors houses dropped down into the 30's over the past day. Yes the Honda is expensive. I've read plenty of comparisons between the cheaper competition and the Honda/Yamaha product. The cheaper competition is sometimes "almost" as good, and sometimes not even half. I've got three kids under 2 at home. My elderly parents and inlaws both have parallel EU2000i setups that run their entire houses flawlessly. I've always had good service from top shelf products. I've been burned rolling the dice on cheapies. Never again. I should say also that running a whole house on a relatively small generator requires some power management and commonsense. My entire house is CFL's and some LED's so the load from lighting is minimal, even so, if I'm not using them I turn them off. Same with any other load, use when needed, use one at a time when possible, etc. Do that and a small genny will do just fine.