A properly designed touring bike with panniers or trailer can haul a lot of weight if you can crank it up a hill. They are built heavier to handle loads and be stable carrying them, as well as have decent mounts for racks and extra water bottles. Also sturdier wheels which are the key to handling loads.
Typically when touring I carry less than 100 lbs, depending on if I am camping or staying in hotels. You really don't need much to "survive" while on a bike, but you will need access to food and water, as you will burn though a lot of it.
I have a 25 mile commute from work, but I could easily bike home and not carry much gear at all. Probably take me 2 hours or so, and I'm not in very good shape at the moment.
As for the comment about bugging away from a hurricane, I recall from a touring list that I used to frequent that when Katrina was coming and all the roads were parking lots, one of the members rode out of New Orleans pulling a trailer and made much better time than any of the vehicles (especially those that ran out of gas). Depending on the terrain and your load (and your fitness), it is fairly common for tourists to ride over 100 miles in a day. I prefer 50 or 60, but I like to take lots of pictures...
Greg