It's an old (and not inaccurate) joke among policy-style debaters that every round must, ultimately, come down to the threat of nuclear war. Even if the debate's about pension reform or agricultural subsidies, one team will find a way to argue that the other side's proposal must inevitably bring about a global thermonuclear holocaust. (Hence the title of R.E.M.'s "It's the End of the World as We Know It," supposedly inspired by Michael Stipe's visit to a policy debate "tournament of lies" and sung in the high-speed style of a policy debater spreading.)
So my first thought upon hearing that Dick Cheney had played that card was: There it is! The nuclear war disad! Except, of course, that these days it's not such a stretch after all. Though when it comes to who's actually got the "disad" here, I think Pandagon's on point.