You can read those excerpts there and the entire article in the above link.
Since American Creation has no "jump" where you can hide the content of long posts, I won't waste space here. Instead, I quote a small excerpt of the NYT article and then my commentary follows. With that:
... “The founders deliberately left the word ‘God’ out of the Constitution — but not because they were a bunch of atheists and deists,” says Susan Jacoby, author of “Freethinkers: A History of American Secularism.” “To them, mixing religion and government meant trouble.” The curious thing is that in trying to bring God into the Constitution, the activists — who say their goal is to follow the original intent of the founders — are ignoring the fact that the founders explicitly avoided religious language in that document.
And here again there is a link to Texas. David Barton specifically advised the writers of the Texas guidelines that textbooks “should stipulate (but currently do not) that the Declaration of Independence is symbiotic with the Constitution rather than a separate unrelated document.”
In 2008, Cynthia Dunbar published a book called “One Nation Under God,” in which she stated more openly than most of her colleagues have done the argument that the founding of America was an overtly Christian undertaking and laid out what she and others hope to achieve in public schools. “The underlying authority for our constitutional form of government stems directly from biblical precedents,” she writes. “Hence, the only accurate method of ascertaining the intent of the Founding Fathers at the time of our government’s inception comes from a biblical worldview.”
On the relationship between the Declaration of Independence and the US Constitution, historians, political scientists and legal scholars on the Left and the Right actually vigorously dispute the matter.
Given the dispute, it's probably not a good idea for history books to take a side, but rather, do their best to "teach the controversy" (and unlike the case with Intelligent Design where you may have heard that line, there really is a compelling controversy here).
Barton and company argue the DOI's status as "law" in an attempt to answer "The Godless Constitution" thesis. The problem is the DOI is not a Christian/biblical document -- at least not in the sense that the Christian Nationalists understand the concept. It doesn't mention Jesus Christ or quote verses and chapters of scripture. Its call to revolution is arguably in tension with Romans 13. And it's not clear that many/most of the important principles enunciated in the DOI have anything to do with the Bible.
The DOI is obviously a Providential or theistic document (not necessarily a Christian or a biblical document).
8 out of 9 members of the Supreme Court (insofar as I correctly understand the newish Justices Alito's, Roberts' and Sotomayor's views) don't believe the Declaration of Independence is "law."
Justice Thomas, btw, is the only member who does.
And most conservative expert figures endorse the "DOI is NOT law position." Not only Justice Scalia (and the late CJ Rehnquist), but also former Judge Robert Bork, law professor Lino Graglia, the late conservative traditionalist Russell Kirk (who notably argued the DOI was a wink towards France to win their support against the British) and many others.
I think they recognize calling for revolt on the grounds that God gives us the "right" to do so isn't exactly a settled position in traditional conservative Christendom and also may not foster the kind of orderly, traditionalist society they desire.
Yes, a "revolutionary" current is fairly well established in Christendom. It's just not clear that revolutionary thought harmonizes better with conservative Christianity, than for instance, liberation theology.
Lino Graglia well sums up how the DOI's call for revolt arguably conflicts with conservatism’s moral traditionalism and vision for an orderly, lawful society:
... The Declaration, however, consists largely of a lengthy indictment of King George III. It is hardly the sort of thing you would expect to find in a nation's constitution. What it is, of course, is a document meant to justify revolution -- that is, illegal action. Having no human law to rely on -- being in defiance of authority -- revolutionaries necessarily come to rely on the law of God, who, happily, rarely issues a protest.
I'm not sure whether Graglia is a Christian, but he could, if he wished, quote verses and chapters of scripture and distinguished orthodox theological arguments on behalf of his sentiment.
Perhaps he, Robert Bork, Russell Kirk are wrong and perhaps the conservative Christians who reconcile the "Americanism" of the DOI with biblical Christianity are right. But, again, K-12 history books shouldn't pick a side in that debate and try to sell it to school kids as Barton wishes.