The only real assumption you have to make, other than the axioms of logic and mathematics which can really be taken as a given as they're part of the language, is Occam's Razor, which is something fairly trivial to assume - especially as it's popped up many times in theology, was created by a theologian and was originally made to prove something about god. Everything else is just window dressing.
What exact kind of ID are they talking about? The faux-science one (with an unspecified entity) or the god one? Bear in mind that there is a significant amount of evidence against both, and there is no true irreducable complexity. In addition, if it's the former, it assumes some science and can be argued against fairly simply from the point that it increases complexity not decreases it.
And so on, and so forth. I must say that this is an innovative and new approach!
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http://meninhats.com/comics/20040825.gif
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WRT what you actually asked, see the above comic strip.