Another one of those American English/British English things: the Brits always say "I couldn't care less". My guess is that the American formulation uses irony and should generally be uttered with a shrug and, probably, a cod New York Jewish accent, whereas the Britspeak version is a straightforward declaration (spoken with a sneer). It does, however, appear that this reversal of the normal BE/AE paradigm causes some confusion, concern and even condemnation in those parts of North America where they don't actually do irony. But quite frankly, my dear, I don't give a damn.
rootbeer277 hypothesises a contraction of something along the lines of "I care little and could care less". Which is a possibility, I guess.