It should take about a week. If I remember correctly (it has been a few years now) I lost about 5 lbs the first week, but I was VERY VERY strict & probably had >10 carbs a day. Also I found myself ummmm......what the heck.....peeing a lot so I know most of that was water weight. After that first week I lost weight pretty fast.
The problem with Atkins is if you cheat just once you basically go back to square one. Your body has to get into ketosis phase to really start dropping weight, which takes about 2 weeks. If you go over 20 carbs only one time you start over again.