Okay, this is what I was able to find. According the resort, there is a Gooding's real close, but I checked them out on yelp and they got horrible reviews (
http://www.yelp.com/biz/goodings-supermarket-orlando) so I did some more searching.
There is a Publix, located about 7 miles away at 2925 International Dr., Kissimmee, FL and a Wal Mart located at 3250 Vineland Rd., Kissimmee, FL 34746 which might even be a tad closer.
The Publix recieved 4/5 stars with 9 reviews and the Wal Mart recieved 3/5 stars with 10 reviews. It appears both are typical for what you might expect in most cities. For groceries/produce/meat etc., you'll probably do better at Publix, but Wal Mart will have a decent selection for other items you may have forgotten.
Link to reviews for Wal Mart:
http://www.yelp.com/biz/walmart-kissimmee
Link to reviews for Publix:
http://www.yelp.com/biz/publix-super-markets-kissimmee-7