First of all, I am extremely skeptical that one day of fasting or only drinking juice is going to make any impact on any toxin build-up in your body. When proponents of a health practice don't have any evidence of a benefit from the practice, they always throw in "detoxification." There are some toxins that can build up (metals, especially), but fasting for a day isn't going to get rid of them, and it's certainly not necessary to help your body deal with the things it cleans out anyway.
It also sounds like you think a juice fast will help you lose weight; even if you don't binge the next day, it's still not going to make much difference in the grand scheme of things, especially since it would be EASY to consume as many or more calories than you currently do even when just drinking juice, since it is calorie-dense.
Dr. Andrew Weil has a good articles on the topic here:
http://www.drweil.com/u/QA/QA300783/
And, just as a side note ... coincidentally I had to do a clear-liquids-only fast for a day last Sunday in preparation for a colonoscopy. That meant water, clear soft drinks (I did sugar-free), non-red jello (again, for me, sugar-free), and non-red juices like apple and white cranberry, Gatorade, etc. It wasn't nearly as hard as I thought it was going to be in terms of hunger, etc. What I found was that, starting in the early afternoon, I was EXHAUSTED. I wasn't sleepy, just had absolutely no energy. It was all I could do to drag myself around the house.
I didn't binge the next day, but my sum total weight loss for the week (I weigh in on Saturdays) was no more than it usually is.