It is possible to drink too much water, but I believe you'd have to drink a very extreme amount. Are you drinking just plain water or something with electrolytes (Gatorade or Smart Water)?
ETA: During my twin pg my OB wanted me to drink 1 glass of water for every hour I was awake, so that was at least a gallon every day if you figure that you sleep for 8 hours and are up for 16 (and yeah right, what 3rd tri pg woman gets 8 hours of sleep).
ETA2: I just did some googling, it's called "water intoxication". Apparently a healthy adult kidney can filter up to 15 liters of water each days, so it's not so much as "how much" you drink, from what I read it's more of "how fast" you drink it.