I am using Gnome 3 with Debian Wheezy. I am looking for a way to make the user ask at least for the root password when using the shutdown button from the menu.
polkit/consolekit can do exactly what you need. Write a new polkit rule:
add the following content (assuming you require root password for both shutdown & restart):
Change the privileges on the shutdown command in /sbin so that only root (or a member of a group with equivalence) can execute it. You would make the changes via chmod or the file-manager of choice in your distribution. If you did this, in theory you would have to "sudo shutdown -h now" and you would be prompted for the root password. That should work in theory
Another more complicated but better answer:
Got help from here: http://answers.yahoo.com/question/index?qid=20080606143849AAONUy9