I am not sure if it will cause any problems, per se, but I know from personal experience that your body needs plenty of the juice purely for the energy! I find I can easily go thru 10-12 glasses a day. I space it as evenly as possible and have one every time I feel hungry or lightheaded. I think it is also very important to drink the minimum 6 glasses in order to get the full cleansing effect.
Try to drink as much as you can. It will help your body on many levels. :)
Another thought...
By 6 glasses a day, do you mean 6 - 8 oz glasses, or 6 larger ones? I'd say as long you're getting a total of AT LEAST 64 oz of the lemon drink daily, you're good to go.