It's actually probably not an X problem. The problem is likely that no getty is set to listen on tty3. To fix this, go to your /etc/inittab file and find the lines that control the getty processes, they'll look something like this:
Note: check your getty -- Debian may use something other than mingetty, perhaps agetty. Anyway, the first field is the ID (must be unique within inittab, the 12345 are the runlevel list for the getty to be active on, respawn tells it to rerun on exit (this is why the login prompt keeps coming back up after yo logout) and the last field is the command. Your job is to make sure that there is a getty active for tty3 for whatever runlevel you are in. You'll need to edit inittab and use "telinit q" to tell init to re-read the inittab. Then you should be set.
BTW I'm really tired and have to get up early tomorrow, so I hope this even makes a little bit of sense...