Warning about disk being full

Summary:
If the disk is full to the point of preventing a user login, Ubuntu (regardless of it being Xubuntu, Kubuntu, Ubuntu, or Edubuntu) should warn the user that files should be deleted or removed before rebooting or logging out.

Rationale:
A full disk or full /home partition (if there is one) prevents a user from logging in graphically. It's a similar rationale to bullet-proof-x--most desktop users do not want to have to use only a terminal to troubleshoot problems. They can always opt for a terminal, but they shouldn't be stuck at one.

Scope and Use Cases:
This just happened to me, actually! On my laptop, my / partition was relatively small, and I was playing around with installing a lot of packages, to the point where my / partition was almost full. When I rebooted, I got to the GDM login screen okay, but when I tried to log in with any user (on any window manager or desktop environment), I got the message about my session lasting less than 10 seconds. I was told to use failsafe mode and check my ~/.xsession-errors.

I wasn't able to log into failsafe Gnome, and I got the same message. When I logged into failsafe terminal, I could see the error message indicating there wasn't enough space on "the device."

Since I have a little experience with Ubuntu, I knew to do
Code:

sudo apt-get clean

to get rid of all the extraneous .deb files in /var/cache/apt/archives, but how would a regular end-user know to do that?

Here's another example of a user running into the same problem:
session lasted less than 10 seconds

Implementation Plan:
Just as the power manager will warn you if your battery is running low, something (God, I'd hate to have another applet, but maybe that's what it should be...) should pop up and let you know if you're running dangerously low on disk space, to the point of not being able to log in on next reboot. A simple pop-up.

The next step, of course, would be for the pop-up to give you an easy way to remove unnecessary files by presenting you some easy-click options for freeing up space (Clean out the /tmp folder, Remove installation .deb files from /var/cache/apt/archives, etc.).