Personally, I don't see why ID is irrelevant to discussing whether or not a large part of the population believes the earth is 6000 years old or not. ID is one of the biggest topics when it comes to evolution and the news. For many people who believe in creationism and take a literalist view of the bible, 6000 years is a common theme and like photon said, it's been mentioned in interviews and news clips with American political candidates in town hall meetings, journalist's questions, debates, etc. It's one of the common questions put to people to determine whether or not they take an absolutely literal perspective toward the Bible or if they believe it should be an inspired, interpretive text.
http://www.christianpost.com/article...-literally.htm
http://www.gallup.com/poll/27682/One...ally-True.aspx
If you take the Bible absolutely literally, and you truely follow the genelogies presented in it, you do reach the 6000 years number. Maybe, we're down to 33.333% now? I don't know what you heard growing up as a mormon, but I certainly heard about 6000 years in Church.