Karen Armstrong studied to become a nun, but takes a liberal view of biblical interpretation in her book In the Beginning: A New Interpretation of Genesis:
The true meaning of scripture can never be wholly comprised in a literal meaning of the text, since that text points beyond itself to a reality which cannot adequately be expressed in words and concepts.
I would add that this is a good approach, in a fashion, to the Constitution, which is sometimes considered a type of "American Scripture." Bare words without a true understanding of how to appropriately understand and apply them can lead to faulty conclusions. Just as there is a danger in being overly technical or literal in understanding the Bible (there are two different creation stories in Genesis, each not to be taken literally), there is a comparable problem in the other context. The trying to overanalyze each and every word can be of limited value.
And, given that those behind the Constitution often were strong believers in the Bible as well (ten amendments, even if twelve were proposed, seems pretty symbolic, no?), it is not too much to say they to saw a connection. Of course, some did just what I warn against here, but others in some fashion understood the moral value of the Bible often was more important than a literal reading. Karen Armstrong in her book also takes a psychological view of things, analyzing the inner selves of the Genesis characters. One f-up bunch, they. Even here, yes, looking behind the Constitution to what drives it, such as what drives the First Amendment can be helpful in understanding its application.
Karen Armstrong finds Genesis so fascinating in part because of its realistic view of human nature as well as accepting certain things are mysteries. Again, we are talking about a bunch of very flawed people, people who often are "blessed" (an important theme, in effect Karen Armstrong views in as a means of self-actualization, to find one's place in the world) quite arbitrarily. Why is Noah (who unlike Abraham does not try to save those subject to God's wrath -- yes, Abraham in effect challenges God to not destroy two towns if but 10% are innocent ... better odds than the "destroy them all" sentiments in Joshua or Judges) chosen? Last we see of him, he gets drunk and blames the son that found him there, as if it's his fault that his father was naked in a drunken stupor. There seems also to be a lot of favoring of younger sons.
But, as in Job, the mysteries ways of God are to be accepted as the way of life. This is not that acceptable on rational grounds, but it is refreshing in another sense: even if it is gauche to bluntly say it, God seems imperfect. Humans have free will and do things to bother him, make him angry, and after Noah, God basically is stuck with it. Since God created all, some know deep down that -- as with the presence (unexplained) of that tempting snake (symbolic or not) -- the way of the universe is imperfection. The first chapter of Genesis provides an ideal creation, one with a single God in control that contrasts with more messy pagan creations. But, the latter -- with their flawed deities -- come off as more realistic.
The patriarchs are imperfect sorts as well. Also, women repeatedly come off as important forces, at times in a superior position. Tamar asserts herself when her father-in-law and brother-in-laws fail their duty to bring her an heir [it is her action that leads to the birth of the ancestor of David ... and Jesus]. Action (even if the morality is mixed) and self-knowledge also are honored but faith does not result in easy success. The characters ultimately might win out, but it can take decades, and even then the results are flawed (Jacob's family is a mess; Isaac is a largely sad figure).
And, there are many little fascinating tidbits that advance the story and/or provide insight into the times (or that of those who wrote it -- the Tower of Babel is a takeoff of Babylon, where such a structure was honored; the reader should know that Babylon ultimately defeated Israel). A non-literal reading therefore results in a deeper understanding, one in fact more "accurate," and provides value up to the current day.