Here is a good thread about the honda eu2000.
http://www.candlepowerforums.com/vb/showthread.php?t=172648
The 2000 will easily run your furnace fan and fridge.
I'll say that during katrina we ran:
fridge
deep freeze
satellite dish
tv
2 lights
2 fans
microwave
It's got a nice bonus that the engine's cooling air (hot air) is directed down and back through some louvers. This is an excellent place to put things that you need to dry out: clothes, shoes, frozen food for defrost, etc.
If you do purchase one and have time to wait for it,
www.wisesales.com is the absolute best place. Their prices are rock bottom and they ship fast. I have bought about 6 generators from them.
I have only 1 complaint about it. It won't run all night before it runs out of fuel. Now all these things are excellent on fuel, but the tank is simple a little small at about 1.1 gallons. You can buy or easily make an extended run fuel cap though. Wisesales sells them. Or you can make one with an extra fuel cap, a hose barb, and some fuel tubing.
There is one other model to consider, the yamaha yg2800i. Basically it's a honda eu2000 with a 3 gallon tank, fuel gauge, 50% more power, and 10% more noise all for an extra $200. Wisesales sells these also.
When my honda dies I will take a very serious look at the yamaha.