Well as I was browsing reddit I came across this thread which links to an xda-developers post giving a download link to an apk on how to install Google Wallet on a stock Samsung Galaxy Nexus Device. Right now the Google Wallet application is listed as incompatible in the Android Marketplace for my new Galaxy Nexus but using this method I was able to get it working (Installed correctly both on Wifi and 3G).I will give you my experience and instructions on how to install below.
1) Enable installing of apps from Unknown Sources (In the security section of settings)
2) Install some sort of app that enables you to install 3rd party apps on your phone (Not sure if this is needed, I used Astro File Manager for this task).
3) Download the .apk file to your phone here: http://www.megaupload.com/?d=GQ6YS0KM
4) Install the .apk file using whatever method you want.
5) Enjoy your Google Wallet and free $10
Note: I ran into a few problems (Google wallet has stopped error) which I simply fixed by force closing Google Wallet and then clearing the cache. Interestingly when I did this I had to "re-activate" my google account even though it was already activated with Google Wallet and I received another confirmation email. This is most likely some sort of bug.
After further testing, I uninstalled the Google Wallet .apk and reinstalled it. I also ended up having to get another $10 Google pre-paid card. I am not sure if this is a bug or if you spend your $10 and uninstall and reinstall you will have another $10. I have yet to actually purchase anything using the app but from reading other user responses I assume it works correctly.