I spent some time investigating this issue. Here's what I've determined: for those of us affected with this problem, it appears that we somehow received a botched installation of 4.0.2 (the version we're running currently). What's the botch? Our phones don't have a working recovery image.
You can test this by trying to enter recovery. Turn off your phone. Then, simultaneously press and hold volume-UP, volume-DOWN, and POWER until a screen with an Android on his back appears. This is the fastboot screen. From here, you can choose 'Recovery'. If your phone is like mine, any attempt to go to Recovery will just put you in the dreaded Google logo loop.
So, what's the solution? I'm afraid the only way to resolve this yourself is to unlock the bootloader and do a complete install of the 4.0.4 image yourself. One step of that process is to flash an updated recovery image; this will cure the issue. Fortunately, on the Galaxy Nexus, you can easily re-lock the bootloader with a single command. I have done all of this and can confirm that it works.
If you're not comfortable unlocking the bootloader, the only other way to fix this is to send it back to the vendor. I have a strong suspicion that phones affected by this bug are unable to receive any further OTAs at all. This means Google can't fix your phone by pushing out a different OTA.
Final warning: until this is fixed, you can't do a factory reset, either -- that process will fail because it, too, uses the recovery. So don't plan on selling your phone on eBay until you get this fixed.