One thing might be in our favor. Not everyone hunts like they used to. Lots of people won't have what they need to take game, whether because of their personal beliefs, stupidity, or gun laws. Game will get smart quick once you get a bunch of Elmer Fudd's in the woods making all kinds of noise.
Another thing may be in our favor as well, at least for those worrying about people pouring out of large cities. The majority of these people aren't going to consider hunting right off the bat, they're going to eat everything in the city that they can beg, buy, or steal. Think of how many of them do nothing but sit at a desk and peck buttons on the computer all day. Are they going to have the stamina to walk if there is no gas, the several days to a week all the way to where game MIGHT be, spend the time to hunt, know how to gut the kill, and then have means to take all of that back to the city to their nest of whatever?
Humping a deer out of the woods and then however far back to where they are located isn't child's play for the underfed, out of shape, mental fried city dweller. Hell it's not child's play for most anyone.