When is too much of a good thing too much? In the case of exercise sometimes we tend to push ourselves just a little to hard. The consenquences destroy ultimately what it is you are trying to achieve.
Train Smart, try to keep most of your workout sessions under an hour if you can help it. And if you do go past the hour be sure to hydrate with something other than water, a good sports drink would suffice.
Listen to your body. You know your own body better than anyone and when it tells you it has had enough then listen to it. Make sure to distinguish between feeling lazy and feeling fatigued....there is a difference.
Hydrate. Drink at least 20-24 oz of water prior to training and be sure to hydrate regularly during exercise. At least 7-10 oz every 15 mins or so and 20 oz or more for every pound of water lost post workout.
There are many symptoms of overtraining and everyone is different. Feelings from anxiousness, malaise, lethargy to feeling that even when you want and need a day off from training that you can't stop. It varies greatly by individual, just be sure to listen to your body you know how you feel when the training is "just right"
In conclusion, yes it is important to push yourself in order to make your fitness goals, but push with a broom not a bulldozer!