What was wrong with the 3ds? If it was negelated (dropping it/breaking it) then they won't fix it but if it's an manufacturing defect then it only takes them a week or less to fix.
Well, that's only if you tell them that you dropped it. I guess it depends on the type of damage, but I dropped my DSi XL a while ago and it broke the R1 button (when you pressed it, it wouldn't depress after). I explained this problem to NOA, but I *FORGOT* the part of me dropping it onto a hardwood floor. 3 weeks later, completely fixed, and NOA paid for the shipping to and from. Nice.
And I wouldn't feel guilty about this sin of omission. I mean, you're not going to suddenly stop giving Nintendo your disposable income anytime soon, are you? I sure haven't.