I forget which supermarkets do this, but some of them, for a fee, will deliver the groceries you want to your resort. The fee might be the same as the price of a cab, plus they do the work for you, so you're not spending your vacation time in the market. You can order and pay online, and they handle the rest. I believe Gooding's is one of them.
Meanwhile, the DVC resorts all have a tiny selection of groceries available (since all the rooms at least have kitchenettes), usually in their respective gift shops. Not a great selection, and certainly more expensive for most items than a sueprmarket, but potentially easier to get to and from. Someone can correct me on this, but I believe that the water launches that go from PO-R to Downtown Disney also makes stops at both POFQ and Old key West, which is a DVC resort and as such would have a slightly better grocery section than POR will. If I'm right about the water launches, then you could, as a suggestion, make reservations to dine at Olivia's, the restaurant at Old key West. While there, you can stop at their shop and load up on some essentials, then go back on the water launch to PO-R. The general stores at Fort Wilderness also have a better-than-average selection of groceries, and you could potentially go there for dinner one night, stock up on your essentials, take a bus to DTD and then a bus or water launch from there to PO-R. Not the easiest solution, but it keeps you onsite, and it affords you opportunities to visit other resorts, which I enjoy doing, personally.
EDIT: Apparently, gardencrocer.com has better prices and a delivery fee of only 12 dollars compared to gooding's 25 dollars. If ou buy at least 200 dollars in groceries, delivery is free, but I'm guessing that might be more than you'll need.
