I think it depends on what you mean by "as we know it." I think the human spirit in general and the American spirit in particular is incredibly resilient. I do not believe even several nuked cities will cause the country to be destroyed.
The principles upon which the nation was founded - although atrophied by modern society - still exist, and are cherished by many. And they don't depend on gleaming cities to exist or flourish.
I hope my opinion is never tested, since I live in LA and would have to watch the drama play out on a celestial television. :-)
When I say "As we know it" I mean we'd be facing complete military control of the government, suspension of basic liberties out of necessity, martial law, suspension of the Constitution for the forseeable future, In short we would be living in a police state for the rest our lives, and probably for the lives of our great grandchildren.