No USB Storage Mode on GalaxyNexus running 4.2.2
Normally you would put the device into storage mode. When the phone is normally booted without storage mode you'll only be able to see internal, then when switched to storage mode you'll see the sdcard as well.

But VerizonWireless says the Galaxy Nexus doesn't come with USB storage mode. According to them you would transfer your data/files to PC across MTP. 

So having the external SD card not show in PC explorer, can be bypassed by inserting it into a card reader on the PC. A little inconvenient, but will accomplish your task.