American here. I always assumed it was a corruption of “I couldn’t care less”. And it’s one of my pet peeves, I agree it means the opposite of what people think it means.
This gained popularity in Australia about 15 or so years ago. It started out as "I could care less, but it would take an effort’ or something similar. Basically I’m not completely disinterested, but damn close. From there it got shortened to “I could care less”, which is thankfully not heard much. I assume something similar probably happened in the US.
The words to not literally mean what the phrase means. It almost certainly sprang from “I couldn’t care less,” but somewhere along the way, the n’t got dropped.
Similarly are the phrases “lock and load” and “head over heels,” both of which were flip-flopped over time.
I used to bite people’s heads off when they used this ridiculous phrase, figuring it was, indeed, a nonsensical abbreviation of “I couldn’t care less”. Then, however, I realized it COULD be interpreted as, “I could care less…” as in, “I could care less, but it would be difficult”. Not as likely, I think, but food for thought, perhaps.