Grab this .apk file from the XDA forums and sideload it like you would any other app. The instructions state that it will work on unrooted devices, and CNET actually ran an article detailing this a little while back. The original XDA thread is here, the link you need is the one under the QR code (the "APK method").
This particular method will evidently only work if you live in the US and have Android v4.0.2 or later installed, but that should cover any typical VZW Galaxy Nexus at this point.
As far as I'm aware, you will not be able to get updates from the Play Store if you sideload like this, but that is the only caveat I've personally encountered thus far on my VZW Galaxy Nexus. I used the free $10 prepaid balance at McDonald's without any issue.
A few additional musings after doing some experimentation: after sideloading the .apk above I was not able to update Wallet from the Play Store app on my phone. However, if I logged into the web store and visited the page for Wallet, it listed my Galaxy Nexus as compatible. Hitting Install on the web page allowed me to push the updated version to my phone successfully, despite the fact that I could not do it from my phone.
If you're itching to try out the newly added ability to add your credit card to Wallet, you could try the above to get yourself updated to the newest version. Alternatively, if you consider me a "trusted source" (I'm trustworthy, I swear) you can get a copy from my Dropbox account. I simply pulled the updated .apk file from my device after I updated through the Play Store, so I can safely say this version has not been tampered with by any third parties.