It survived Hurricane Katrina, which created devastation similar to a nuclear weapon, albeit with a somewhat lower (though still very significant) death toll.
I think it would matter a lot which city. A nuke in Manhattan? Forget it - there goes the stock exchange, most financial firms, Madison Avenue, 11 million Americans, and the most recognizable city on earth. DC? There goes the government. Cleveland? We'd probably be okay.
Something like Boston or SF would be borderline - it'd be a tragedy, but the country would survive. I wonder what a nuke in Silicon Valley would be like though: a large one well-placed near Sunnyvale would take out Google, Apple, Facebook, EBay, Adobe, and Yahoo.
