This is for the Verizon LTE version of the Samsung Galaxy Nexus.
I am tasked with writing a tiny app that will effectively disable/enable 4G capability. This can be done
All the other answers are correct that this requires access to Settings.Secure. Take a look at how the phone app handles this setting https://github.com/dzo/packages_apps_phone/blob/master/src/com/android/phone/Use2GOnlyCheckBoxPreference.java
or take a look at the Toggle2G
app source:
https://github.com/TheMasterBaron/Toggle-2G