As you know, Galaxy Nexus supports only MTP protocol for USB connection, which is not greatly supported under Linux. As a workaround, I have tried to upload my music to Galaxy Nexus through WiFi. I have installed "WebDAV server" (The Olive Tree) from Market and uploaded a couple of tracks to Music folder. But, Music app on the phone does not see any music, shows just "ways to add music..." message. Is there a way to force a rescan?
Specific solution for my problem is to install Rescan SD application from Market and launch it after uploading music through WebDAV.
I suggest you to try QtADB, instead of your WebDav work-a-round.
I tried every way and this is by far the best.
I have to admit I have not played with Galaxy Nexus, but AIRDOID is claimed to be a good solution for moving files. I use it with both my phones and works fine. I know the new way parts are mounted makes a huge difference. I usually use Zimly as media player, and it finds uploded with airdroid files without any problems. You might need to re-scan media, as well.
If you are on Ubuntu, you might try this as last resort solution