Susan, in most circumstances it is illegal, or at lease considered unsporting to shoot a bird unless it is on-the-wing. So a shotgun gives you a chance, though it is not by any means as easy as you might think. Rabbits and other small mammals are fair game with most firearms.
Of course in a survival situation, who cares about being sportsmanly.. use whatever you have!

Yes, if you're too close with a shotgun you can make a mess. And yes, there may well be shot in the meat (with all the dental implications). I have a friend who duck hunts, and X-rays his kill to find any stray shot.But he's a Vet. and has the machine to do this at little cost.