Our beloved Crunchy was on the right track when he tried to get at the truly interesting part of the debate about Obama’s Christianity: what it says about the relevance of orthodoxy.
But I’m not wild about the typology he creates for Christians. He believes that most Progressive Christianity amounts to “Moralistic Therapeutic Deism”:

Progressives think that religious truth is indefinite and subjective, and can change according to the perceived needs of people in a given time and place. Traditionalists believe that religious truth is definite and objective, and can be known with some degree of certainty.
Put another way, progressives tend to think that religious truth claims are statements of an individual’s thoughts and emotional state; trads tend to think that religious truth claims are statements about metaphysical reality.

As I understand them, Progressive Christians believe that while some aspects of the faith ought to change over time, others are immutable, objective and permanent. Most would say the never-to-be-altered-regardless-of-current-fashions-or-emotions point of Christianity is something like: Love Thy Neighbor.
They believe there are a few key meta-truths to the Bible and that the other stuff is subject to interpretation. They tend to believe the Bible is inspired by God rather than the literal word. They often read the Nicene and Apostles Creeds as being human creations that capture some of the basic truth of Christianity, but miss others and elevate certain concepts to a literalness that Jesus probably wouldn’t have wanted.
By the way, this was also the view of Jefferson, Franklin, Adams, Washington (probably), George W. Bush (implicitly) and most modern American Christians.
Having said that, I would love to hear from some progressive Christians on why John 3:16 doesn’t make the short list of Christian fundamentals.