Anyone notice their Nexus taking a long time to charge? Mine takes about 5 hours to fully charge and it is impossible to use while plugged in. It gets ridiculously hot. It shut down Angry Birds after 10 minutes while charging I'm guessing due to the heat. I'm only getting about 6 hours of moderate usage out of the battery.
Outside of the battery life, I love everything about this phone.
My guess is that you have a faulty battery. If you have zero issues otherwise with the phone, I would ask for a new battery before exchange the entire phone.
My phone does not get that hot and charges very fast compared to previous phones I've owned.