Watching a season of the "Survivorman" show impressed on me just how darn difficult it is to "live off the land" so to speak, unless you're already established with a garden/crop/livestock or something.
If anyone's not familiar with the show, it involves a survival expert being left in the wilderness (forest, jungle, desert, etc) under conditions in which someone could plausibly be stranded out in the wild. He carries video equipment and self-documents everything he does.
After a week, he gets "rescued".
I have to say, in most of the cases he looks pretty bad by the end of the week, and he usually admits it too. It doesn't look like he'd make it a month. And he's a survival expert, so I'm under no illusions about my long term odds out in the wilderness. Think I'd stick to the cities in such a scenario as you describe.
Should be stray cats, dogs, squirrels, and so on that are easy pickings for a .22 rifle, once all the normal food supplies are gone and there's nothing left to scavenge. Course, this also depends on how many other humans there are competing for the same resources.
I think for long term survival and defense people would have to band together again just the way it was done in the hunter/gatherer days. A lone guy or two by himself isn't going to last long before something does him in.
There would be mass die-offs of people, and individual survival would probably depend more on luck than anything else (edit: I mean luck being a factor in loooong term situations... preparation is still the biggest factor otherwise!) but enough people would be able to pull it off to keep humanity from going extinct. That is, unless we're also being hunted down by Skynet at the same time. Then we're screwed!!