I lived in Sitka quite a few years ago, and while I was there I helped out in a gunshop. We had a customer come in who constantly went to the other islands to hunt deer with his .223 Remington. He wanted us to build him a custom load that would stop a brownie, we thought to ourselves that he couldn't possibly be serious, but in fact he was, we contacted Sierra Bullets and their reaction was much the same as ours. Needless to say we didn't get too involved with this suicide hunter. But the natives up there (in Alaska) have for many years taken brown's, grizzly, and polar bear with .22 hornets, now before you call me a liar, they will approach the beach in a boat with the motor shut off and shoot them through the eye at less than 50 yards out. If they just wound it no matter they aren't required to chase it down.
Now to answer your question, the largest game I would attempt to take with a .223 would be a 350lb talabani.
lol
Really, a careful shot will take down a deer sized animal pretty well, you just need to make sure that the bullet construction is adequate. And that your state allows it for the species you desire to take.
good hunting
dave