The same with mine back in December or January. The battery issue is why I returned within the 14 day return period and I paid the $35.00 restock gladly. I waited for the Samsung S3 and I am very happy with it. I always get about 12 hours out of my charge the voice and data work well. I really did not have any other issues with the phone other than the short battery life which was not acceptable to me. Good luck with your Nexus, I would take it back and get something else, a razr is a much better phone. If you want something with a very good battery life try the Razr MAXX. Both good phones. The S3 is a good phone as well but somewhat expensive. The problem with the Iphone is it does not have LTE at this time.
The screen on like with any device is what really kills your battery. Also you may not be a power users but your device might be. You may have open apps that run in the background and so they continue to run.
I don't do anything special and on an extended battery I get 18-30 hours depending on how many phone calls/text and emails I do.