Does the new pleading regime of Iqbal and Twombly apply to affirmative defenses?

Most litigators know (at least they should) that a pair of recent U.S. Supreme Court cases (Iqbal and Twombly) effectively heightened the standards for pleading causes of action in a complaint.  In the old days (i.e., the early 2000s), a plaintiff's lawyer could just throw together a complaint with a skeletal set of conclusory assertions to match the elements for each cause of action.  Now the Supreme Court has interpreted Rule 8(a) of the Rules of Civil Procedure to require that "a complaint must contain sufficient factual matter, accepted as true, to state a claim to relief that is plausible on its face."  This "plausibility" requirement sent shockwaves through the plaintiffs' bar.