Cullen Murphy speculates about what sort of literature produced today might go into something like what the Bible now is if they were to be compiled into a great work that could serve a similar purpose for people of the future. I think some of his analogues are pretty far from the purpose of the original, and he's got some glaring omissions (Tolkien, the U.S. Constitution, a few key modern philosophers, of which he has none listed at all). Also, he's assuming secular society would be producing this. Some of the works are remotely religious, and perhaps Emily Dickinson's parallel with the psalms is adequate for that, but there's nothing really theological to be an equivalent of Romans or Ephesians.
One of the problems is simply that nothing really parallels biblical works. The closest thing we have to the Song of Songs would be smutty romance novels, except those are far removed from the spiritual significance applied to the Song of Songs by the typology of love themes in the Hebrew scriptures. There's never been any literature produced that's even close to what the Gospel of John is up to. It's simultaneously a story, an argument, an extended teaching, and a set of overlapping and interactive metaphors and other poetic imagery. Those who have tried to do such things have failed to produce anything quite so magisterial, and they usually have no spiritual significance whatsoever. We would need tales of the past heroes of the people but also accounts of the failures, and these would need to be constructed so as to be making a theological point (or at least something like one). Then there's also the issue that literature today would have to include more than just the printed word. Would things like Star Wars, Saturday Night Live, Friends, Gone With the Wind, Seinfeld, Cheers, X-Men, Sesame Street, Survivor, and Wheel of Fortune be in it?
Despite all this it's interesting to think about what literature of our time fills some of the roles that biblical literature filled for the ancient Hebrews and early Christians. For what it's worth, I think the biblical literature itself fills many of those roles for contemporary Christians as it is and in a way better than anything else could, but that misses the point of what's being done here. It's an attempt to find what represents the culture of today in a way that the Bible represented cultures of the past. That misses so much of what the biblical books are all about, though.