The American Founders wisely recognized that soteriology---the business of salvation---is not "political theology," which is how man should live, and his duties to his fellow man in this world. In fact, the "fellow man" part is precisely where there the Christian political theology is located. But when it comes to salvation, you're on your own, man. No government ever got anyone into heaven.
It's agreed between Aristotle and Aquinas, and even "state of nature" early modernists, that man is a social animal. That's the key to the philosophical history about the nature of man. All political philosophy must flow from there, or else it's just singing "We Are the World," which is a nice sentiment, but not reality.
We're not hermits by nature---because every hermit is "free." We're not tiger or polar bear males that eat their young, yum. And mostly, we are not mantises or Black Widows that eat their male mates for the good of the children either.
Historians like Barry Alan Shain argue that the Founding-era understanding of "rights" was not the radical individualism of modern political philosophy [John Stuart Mill, etc.], but communitarian: the smaller community has its values, and the imposition of a "larger" community---a national government, the "state"---might use its overarching power to destroy the very notion of "community." We all become drones in the Universal Homogeneous State.
On the other hand, on behalf of the individual, natural law, imago Dei, and a posteriori observations like Adam Smith's Wealth of Nations ["squashed version" here], well worth your time] all argue that man is best when he is free, and further, that society is best [healthiest; vital; dynamic] when the individual is free within the sphere of "ordered liberty."
This was the Founders' view, sometimes called "classical liberalism."
One might accuse "ordered liberty" of being oxymoronic, but it's a "golden mean."
After all, a well-functioning society is good for the individual as well, even if he's not as "free" as Caligula. Free individuals make for better societies. We are not ants, afterall.
And Caligula's unmoderated freedom was bad for even Caligula himself. Surely he was unhappy; dude had no eudaimonia. Caligula was such an unsocial animal. His "freedom"---and was any man ever more "free" than Caligula?---isn't what the Founders meant by freedom.
Now it's true that Jesus was apolitical, and soteriology was his ultimate
message, the next world, not this one. Still, the corollaries for political theology are accessible to [right] reason.
As for tyranny, John of Salisbury in Policraticus [1150 CE, a pre-Gutenberg bestseller] is already on the path toward "resistance theory"; the Calvinists [more precisely, his Reformed Theology successors Theodore Beza, Peter Martyr Vermigli, Mornay[?], John Ponet, Lex Rex Rutherford, and the Phillies extended their winning streak to eight games and just traded for Roy Oswalt, who starts against the Diamondbacks tomorrow] provide the theological argument, and not a small amount of military heft, in the English civil wars of the 1600s that were a dry run for the American Revolution.
Resistance to tyrants is obedience to God. Why? Because tyrants are all about their own good, not "the common good." Now, the odd thing about the "Calvinists" is despite their rigid theological doctrines of predestination and "the elect," their political theology still arrived at no distinction on this earth between how one should treat "elect" from "non-elect." Soteriology is not political theology! You treat the "unelect" the same as the elect.
This is the Christian political theology. One cannot do justice to Christianity merely with sola scriptura or the neo-Lutheranism of Karl Barth, nor as a mere Hobbesian political arrangement, where man's religious impulse must be subordinated to and controlled by the "state."
The Founders rejected both poles.
We must do justice to Christian political theology in our discussions of the Founding, or speak of Christianity not at all, which, admittedly, many folks these days prefer not to.
But we can't trot out a one-size-fits-all caricature of "religion," as if Christianity is no more than the Flying Spaghetti Monster or some Kiwanis Club. That's not "Christianity" as the Founding era understood it.