Ultra low power 555 timer circuit
Since low power is a important criterion, don't use the evil 666 555 timer.  There are much better ways, including a few discrete parts.

If this problem came up in the real world, I'd use a tiny microcontroller like the PIC 10F200.  It would stay in sleep most of the time.  A button press wakes it up.  This causes it to turn on the LEDs, wait 20 seconds, turn the LEDs off and go back to sleep.  There are other PICs that are a little larger but have even less sleep current.  You should be able to get this down to below 1 &micro;A worst case.