Food is massively expensive there, a lot more than I expected, but there are alternatives. As FZR said, Val D'Europe is only one stop away on the train, which is probably the cheaper option if you're staying in the Disney hotels.
When I went we stayed at Davy Crockets Ranch. The kids loved it and it actually ended up saving us a heap on food as you get given so much stuff for breakfast that you can't possibly eat it all.
For each breakfast (that you collect fresh every morning) we were getting 6 croissants, 6 pain au chocolate, 1 long french stick, various jams and spreads, tea and coffee, 1 litre of orange juice and 1 litre of milk.
We found that we could use the croissants and chocolates for breakfast along with a cup of tea, and then we used the orange juice, french stick and spreads for lunch. We did a small food shop in the little shop there which wasn't actually too expensive for bread, pasta, etc. but a lot of our main meal stuff was purchased in Tesco before we left and taken with us.