That depends on what you consider walking distance....
There's not really anything that's closer than a couple of miles away. You'd have to pack whatever drinks you want to bring on board and lug them with you on the plane, something we've only done once, then decided it's not really worth it. I like to carry as little as possible with me on to the plane, and I don't know that I'd trust a bottle of wine to remain intact in my checked baggage. You could probably get some bottled water in the airport concourse, it's kind of a mall, of sorts, but I don't think there's anywhere in there to buy beer or wine which you could bring with you.
What you can do is shop during your first port call, you're in port on the first full day of the cruise on all but the 7-day eastern itinerary (either in Nassau or Key West), and can stock up then.