In reference sources such as The Triathlete Training Bible, they stress the importance of recovering from your workouts. When training hard, your are breaking down your muscle fiber and you need to set aside down time to allow them to rebuild. Most of the literature I have read suggest taking at least one day off to recover. But I suppose that all depends on how hard you train and how you feel the day after. As far as overtraining goes, yes you can overtrain. What happened to me was I was riding a very hilly course very hard several days a week. When my knee started hurting, my doc said it was because I was overtraining and strengthening only the muscles that in the front part of my knee. This caused an imbalance and pulled my knee cap to tightly against the ligaments and caused a burning sensation. So, balance is important and listening to your body is important. Because yes you can over do it.