I have spent more time than any sane person should contemplating on just what I would need to survive should civilization as we know it come to an end.
The short version of my conclusion is that there is no way I would make it. A select few hardy individuals might survive for decades, providing they don't get appendicitis or do something stupid with firearms. But you would need to be extremely competent, live in an extremely good location and have lots and lots of really good luck.
The solution, obviously, is to survive together. Not as a family unit, as pictured above, but as a society. Rob Hopkins, of the Transition Towns Initiative, has some enlightened views on this subject.