This has happened to mine and my wife's gnexs'. I googled "sprint galaxy nexus MMS problems" and found it could be an APN problem.
I discovered a thread on android authority with a potential answer. I downloaded APN backup and restore from the play store and tried converting it to a system app with titanium backup pro like the thread said. It gets stuck in a loop and never completes.
Sent from my Galaxy Nexus using Android Central Forums