For two adults and two children (and not having to constantly worry about wether or not you have "enough" ) - $125.00 - 150.00 per day. That's for a combination of counter service and sit down meals all inside Disney. The cheapest meal we had was at Columbia Harbour House - two kid meals, one adult fish/chick. combo, drinks for 4, and one side item of cole slaw came to about $23.00. As the second adult, I ate the cole slaw and shared a chicken finger off the kids plate.
The most expensive meal, Cinderellas at $74.00 including tip (breakfast).
Most of our meals averaged 40 - $65.00.
To cut cost, try bringing your own drinks (which will set you back $2.50 per person in most cases). Also, share meals if you are not a big eater.