Between 2.75-to-3.25 hours prior to your flight time.
If you are taking an international flight you'll be scheduled 4 hours before flight time.
There was a span of just a few days in August 2006 when DME was picking up domestic fliers 4 hours in advance, in the days following the discovery of that terror cell in England that was planning to use liquids for bad purposes. DME picked up early on those few days because of the HUGE delays at security, back when there was a lot of confusion and fear and no set guidelines.
So anything you've heard about DME currently picking up 4 hours in advance in inaccurate unless the person was talking about an international departure.