Hi, Todd! You will find a limited supply of groceries available at the Walt Disney World resorts. You can find small cartons of milk, some dry goods, and usually things like cream cheese and peanut butter - but in small sized containers.
There are two grocery delivery services in the area that I have used personally. The one I rely on most often is gardengrocer.com, and have found them easy to work with and very prompt in their delivery times. Deliveries are made directly to your resort, and you have a two hour delivery window, so you are not losing a whole day at the park to wait for the delivery.
The other service I have used is WeGoShop.com. I haven't used them as often, but found them to be a great service as well.
There are taxis available at each resort, so you could take a taxi to a local grocery store to do your own shopping. If you just want to pick up a few items that you can find at a convenience store, your cab fare would be less than $20, as there are mini mart type of convenience stores right near Downtown Disney. There is also a large Gooding's grocery store just across from Downtown Disney, although the time it takes to get in and out of the store will probably end up costing more than a $20 cab fare, and their prices are a bit high.
The grocery delivery services require about a 36 hour notice to deliver, but you could wait until you arrive, see what's available at your resort that suits your needs, and then decide if you need a full grocery order from somewhere.
I hope that helps!