If you are using the latest vlc, 0.9.6, just, go to Streaming, Capture Device, under Audio Device name pick Stereo Mix, or something similar to that, if you have Realtek HD audio, you will have to change it to Stereo mix in the Audio CP first. It will capture all the sound that your computer makes though so if your just streaming music it should work fine.
Is it possible that you can guide me? I can see a function called "Open Capture Device" under the drop-down menu "Files". Is that the one you're talking about? If I click that I don't know what to do next? I'm on 0.9.6 for Intel Mac.