After yesterdays exciting DOOM 3 going gold announcement, id's Todd Hollenshead sent out some infomation about a possible demo, "our priority was finishing the game first and now we are turning our attention to the demo. I don't have any information to share regarding any specific content, but I don't believe that we have ever disappointed in that regard in the past. We will release the demo as soon as it's done, but this probably won't happen until after the game has arrived on U.S. store shelves."
News source: Worthly Playing