This is a hard question to answer as I generally budget $50 per person per day for 3 meals/snacks if everything is bought at Disney.
General Budget:
$7-$8 for breakfast
$10 Counter service lunch
$27 buffet dinner (includes tip)
$5.00 snack
However, this saves money as well:
$7-8 for breakfast
$23 buffet lunch/tip (late usually around 2 or 2:30)
$10.00 little something from counter service for dinner or
less if just want a snack.
Budgeting works better if you eat breakfast in your room. Cereal, breakfast bars, poptarts, muffins and fruit can be easily pruchased offsite and stored in your room. Water, milk, juice and other snacks (chips, pretzels, candy) are also great to keep in room and take into the parks (really cuts cost down). $50 at a grocery store goes a lot farther than what breakfast will cost for 4 adults and 2 kids the length of the trip. Your best bet is to go for the later buffet lunch (say 2 p.m. most days). By that time your starving from walking the parks for awhile you'll be good and ready to eat a lot of food (get your money's worth) and be stuffed for a while after. I find that when I do this, I generally don't like heavy food and will just want someting lite around 7:00 at night.
I say worst case scenerio is to at least budget between $40 to $50 per person per day.