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I think this is a key point:
"White House spinmeisters are used to frontal assaults on their policies, which can be rebutted with a similar set of talking points. But there is no easy answer for the ironist."
To rebut a frontal assault requires no engagement with the arguments or facts or reality underlying the assault. Such a rebuttal can, in fact, be composed before the assault even begins, it's so disengaged from the content of the assault.
For a rebuttal to an ironic attack not to sound like a non-sequitur, however, requires that the rebutter first unpack for his/her audience the underlying points of the ironic attack. And at that point, you either have plausible answers or you don't, but you can't just ignore the questions and plow ahead with your own spin.
This is why irony is so dangerous - the person or institution you attack has only two options: face you and acknowledge your points or consciously concede defeat and retreat. There's no spinning option.