It's real easy to find places to eat, in the area you want to be, especially if you can be flexible, as a PP stated. You can always check either your resort concierge (if you are staying on site), guest relations at the parks, the Disney dining website if you have a phone with internet or just walk up to a restaurant and ask if there is anything available.
On our recent trip I was often looking at the Disney dining website to see if anything was available the interested us more than our scheduled ADR. Also, our flight home got canceled (due to the snow storm in the Northeast at the end of October, we had an extra 3 nights) and I had no issues adding a couple of decent ADR's at prime dining times. Of course it was just 2 of us and it was a quieter time of year and it was before the new cancelation policies really took place (however, I did need to give a CC number to 2 of our ADR's that I normally wouldn't have needed to).
Long story short, if you can be flexible as to where you eat and when you eat, it could be pretty easy to find something on short notice.