The lid doesn't come off easily by itself. You need to remove the whole compartment, and then the lid may come off (I never looked that closely at mine when it was removed). Unfortunately, you will need to remove the entire stereo to get the bin out. There is a write-up here on removing the stereo:
http://www.nicoclub.com/archives/altima ... stall.html
It used to have pictures, but those links have since been broken. I'll see if I can get someone to fix the images. Once the stereo is out, the bin should pop out (but will take a little bit of force). Note that there is a power outlet in there that will need to be disconnected before the bin can be completely freed from the car.