Short answer: You don't have to use MTP; you can use PTP.
By now it is no secret that Galaxy Nexus does not mount as USB mass storage for some wise technical decisions made by the Nexus developers. Now there are a plenty of posts floating around on how to install software in Linux to enable MTP access so that you can access the files from your Linux.
None of those worked for me, partly because of the fact that I am running Linux-Mint 10, and the libmtp that comes for this version is outdated. I can do some hacking to update my version of libmtp, and hopefully work. But, as much as I love Linux, and OSS in general, I hate to give out instructions that require compiling, editing config files, etc.
So the simplest solution that worked for me was to use PTP instead of MTP. Choosing this option causes my Nautilus file explorer to immediately identify the phone as a photo source. And voila, you can now open a file explorer and browse, add, remove files from the phone.
Savor the screenshots to get an idea how easy it is to use PTP to access the files as compared to compiling code and what-not.