That doesn't sound right. I had to root and install a custom ROM to get Jelly Bean on my (Verizon) Galaxy Nexus, but I have family members with (also Verizon) Galaxy Nexuses that are unrooted and have locked bootloaders. They've already got 4.0.4.
Have you tried checking for updates in the settings? Maybe your girlfriend dismissed the update notice.
I checked the update notice. It says it just checked now and there are no updates.
Google Nexus is actually not a phone model but a collection of many models which are only invisibly different. Some of them get updates, some don't, even though all are advertised in the same way.
And it is a "yakjudv" (Australian build) according to the System Information app. It seems I'm waiting for some Australians to let the updates through (if they go through at all). When I bought it from Amazon, it was advertised as a "Pure Google Experience".
I think Google really messed up again. The "Google Nexus" should have been a simple and uniform experience, and not a bunch of branded-phone-hell.
I understand your eagerness. I had been mashing my update button for several days after the OTA update was announced. Evidently these things roll out over the course of weeks, which is not necessarily what you would expect if Windows or Apple o/s updates are your frame of reference.
I was able to "trick" my nexus into updating, by clearing the data from the Google Data Services Framework. That seems to work for some people. Unlocking and flashing is an option that some power users take--particularlly those with LTE phones where there is no OTA yet.
I just cleared the data again, forced-stop, and checked for update again -- and it successfully checked and says I'm still up-to-date with my 4.0.1 Android.
It's probably not the answer you want to hear, but you should root it. Rooting and upgrading my cheapo 2.3 phone to 4.0/CCM9 completely revitalized it. Rooting is the true magic of the Android ecosystem.
That OTA is for the GSM model of the Galaxy Nexus, which is for T-Mobile, AT&T, (and most of the non-US countries) and gets its updates directly from Google. The post above is talking about the Verizon model, which does not get updates directly from Google (because you didn't buy it directly from Google), and is instead forced to wait for updates from Verizon. The only other option is to unlock the bootloader and install a community ROM.
4.0.1 is multiple versions behind even the 4.0 branch though. 4.0.4 is already available in the Galaxy Nexus models that run the Google-maintained version.
It is a "yakjudv" firmware which doesn't get updates.
Apparently Google is advertising their Nexus line as auto-update (http://www.google.com/nexus/#/galaxy/features) but then does all of the "yakju" 3rd party firmware fragmentation which invalidates their own promise.
It's still stuck on 4.0.1 with no update in sight...