The Publix is closer, located at 2925 S International Dr.
Approx Taxi fare one way $12-$14 plus tip from CBR entrance
Rather than taking a taxi, many here swear by Garden Grocer or We Go Shop, which will deliver to your resort for a small fee.
Another option would be the Hess gas station less than a mile down the road, if all you're getting is soda and water. (not sure if they carry Pepsi though, Disney is Coke territory)