1 day overstay?

Well, they can deny you entry under Visa Waiver for a 1 day overstay, but they can decide to let it go. It's a judgement call. The problem is that there's no way to know until you try to come back under Visa Waiver and if they decide against you, they'll put you on the next plane back and you won't be able to use Visa Waiver again. Keep your doentation and don't be in too much of a hurry to come back to the US. If you're coming back on the J visa, it won't make any difference at all and probably won't even be mentioned.