We've talked about this book a number of times on my blogs. It's David Barton's bête noire. It's a good book and both of the scholars who wrote it are the real deal who know and cite the record, in my opinion, better than Barton does.
I don't agree with its thesis completely. But here is what I value in it. What I take from it for my thesis: The political theology of the American Founding represented a loss for the forces of "religious correctness" (a term they use). What the authors then do, which is perhaps a step too far, is bring that battle into today's culture wars and associate the late 18th Cen. forces of religious correctness with today's religious right, and America's Founders with today's secularists. I wouldn't do that. Rather, I'd stick with the more modest thesis that the American Founding and its political theology represented a loss for late 18th Century religious correctness.
So who were the losers? Among them Timothy Dwight, William Linn, John Mitchell Mason, and Jedidiah Morse. The religiously correct were the ones who thought the US Constitution should invoke the Triune God, probable in the form of a covenant as the central anchor of the document. It doesn't do that. Also, it would be helpful if, as Mason wanted (when discussing the Articles of Confederation), America's governing document invoked the "law of the eternal God, as contained in the sacred Scriptures, of the Old and New Testament, the supreme law of the United States,..." It doesn't do that either. So what we are left with is victory for religious liberty and pluralism where the religiously heterodox and heterics like the Swedenborgs, Unitarians, Universalists, etc., have their place at the table right next to the orthodox. That's my thesis.