There is a quotation from the British jurist William Blackstone oft-cited in the "Christian Nation" debates that relates to Christianity's relationship to the common law, and also a notion of "higher law." (This notion of "higher law" has been termed the "Brooding Omnipresence in the Sky" by Justice Oliver Wendell Holmes, Jr.) From Blackstone:
This law of nature, being coeval with mankind and dictated by God himself, is of course superior in obligation to any other. It is binding over all the globe in all countries, and at all times: no human laws are of any validity, if contrary to this; an such of them as are valid derive all their force, and all their authority, mediately or immediately, from this original.
But in order to apply this to the particular exigencies of each individual, it is still necessary to have recourse to reason: whose office it is to discover, as was before observed, what the law of nature directs in every circumstances of life; ... And if our reason were always, as in our first ancestor before his transgressions, clear and perfect, unruffled by passions, unclouded by prejudice, unimpaired by disease or intemperance, the talk would be pleasant an easy; we should need no other guide but this. But every man now finds the contrary in his own experience; that his reason is corrupt, and his understanding full of ignorance and error.
This has given manifold occasion for the benign interposition of divine providence; which, in compassion to the frailty, the imperfection, and the blindness of human reason hath been pleased, at sundry times and in divers manners, to discover and enforce it's laws by an immediate and direct revelation. The doctrines thus delivered we call the revealed or divine law, and they are to be found only in the holy scriptures. These precepts, when revealed, are found upon comparison to be really a part of the original law of nature, as they tend in all their consequences to man's felicity. But we are not from thence to conclude that the knowlege of these truths was attainable by reason, in it's present corrupted state; since we find that, until they were revealed, they were hid from the wisdom of ages. As then the moral precepts of this law are indeed of the same original with those of the law of nature, so their intrinsic obligation is of equal strength and perpetuity. Yet undoubtedly the revealed law is of infinitely more authenticity than that moral system, which is framed by ethical writers, and denominated the natural law. Because one is the law of nature, expressly declared so to be by God himself; the other is only what, by the assistance of human reason, we imagine to be that law. If we could be as certain of the latter as we are of the former, both would have an equal authority: but, till then, they can never be put in any competition together.
Upon these two foundations, the law of nature and the law of revelation, depend all human laws; that is to say, no human laws should be suffered to contradict these. ...
There is a problem, though, in the use this of quotation to argue on behalf of American Christian Nationalism, as has been done numerous times: Blackstone wasn't talking about America, but rather Great Britain. Blackstone was also a Tory who took the side of Great Britain against America; he defended the notion of absolute Parliamentary sovereignty in his teachings.
Indeed, one thing I'd like people to understand is that to the extent that America might have been a "Christian Nation" in a political-theological sense, Great Britain was every bit as much, if not more so. The above quotation, again, would be apt in demonstrating that Great Britain may have been some kind of "Christian Nation."
When America successfully rebelled from Great Britain, she retained the common law, but did need to "revise" it for her newfound circumstances. So, for the "American view," you would need to turn to American commentators. While many founders expressed their views on the common law, only two of which I am aware did comprehensive restatements: James Wilson of Pennsylvania and St. George Tucker of Virginia.
America's founders disagreed on the exact nature of Christianity and the "common law" and Law itself. Below I reproduce James Wilson's position. Wilson, unlike others (like Jefferson), did believe that "Christianity" was part of the common law. What he meant by this and Christianity's relationship to "Law" is something scholars debate to this day. I know that my interlocutors and I have spilt much ink discussing and debating the meaning of Wilson's passage produced below. But note the difference between what was reproduced above by Blackstone and Wilson's position:
[H]ow shall we, in particular instances, learn the dictates of our duty, and make, with accuracy, the proper distinction between right and wrong; in other words, how shall we, in particular cases, discover the will of God? We discover it by our conscience, by our reason, and by the Holy Scriptures. The law of nature and the law of revelation are both divine: they flow, though in different channels, from the same adorable source. It is, indeed, preposterous to separate them from each other. The object of both is ― to discover the will of God ― and both are necessary for the accomplishment of that end.
[...]
Reason, say they, is the first rule of man, the first principle of morality, and the immediate cause of all primitive obligation. But man being necessarily dependent on his Creator, who has formed him with wisdom and design, and who, in creating him, has proposed some particular ends; the will of God is another rule of human actions, another principle of morality, obligation, and duty. On this distinction, the kinds of obligation, external and internal, are founded. These two principles must be united, in order to form a complete system of morality, really founded on the nature and state of man. As a rational being, he is subject to reason: as a creature of God, to his supreme will. Thus, reason and the divine will are perfectly reconciled, are naturally connected, and are strengthened by their junction.
[...]
Reason and conscience can do much; but still they stand in need of support and assistance. They are useful and excellent monitors; but, at some times, their admonitions are not sufficiently clear; at other times, they are not sufficiently powerful; at all times, their influence is not sufficiently extensive. Great and sublime truths, indeed, would appear to a few; but the world, at large, would be dark and ignorant. The mass of mankind would resemble a chaos, in which a few sparks, that would diffuse a glimmering light, would serve only to show, in a more striking manner, the thick darkness with which they are surrounded. Their weakness is strengthened, their darkness is illuminated, their influence is enlarged by that heaven-descended science, which has brought life and immortality to light. In compassion to the imperfection of our internal powers, our all-gracious Creator, Preserver, and Ruler has been pleased to discover and enforce his laws, by a revelation given to us immediately and directly from himself. This revelation is contained in the holy scriptures. The moral precepts delivered in the sacred oracles form a part of the law of nature, are of the same origin, and of the same obligation, operating universally and perpetually.
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But whoever expects to find, in [Scripture], particular directions for every moral doubt which arises, expects more than he will find. They generally presuppose a knowledge of the principles of morality; and are employed not so much in teaching new rules on this subject, as in enforcing the practice of those already known, by a greater certainty, and by new sanctions. They present the warmest recommendations and the strongest inducements in favour of virtue: they exhibit the most powerful dissuasives from vice. But the origin, the nature, and the extent of the several rights and duties they do not explain; nor do they specify in what instances one right or duty is entitled to preference over another. They are addressed to rational and moral agents, capable of previously knowing the rights of men, and the tendencies of actions; of approving what is good, and of disapproving what is evil.
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These considerations show, that the scriptures support, confirm, and corroborate, but do not supercede the operations of reason and the moral sense. The information with regard to our duties and obligations, drawn from these different sources, ought not to run in unconnected and diminished channels: it should flow in one united stream, which, by its combined force and just direction, will impel us uniformly and effectually towards our greatest good.
But note, unlike Blackstone, Wilson doesn't use verbiage like human reason is "corrupt," "blind[]," and that "the revealed law is of infinitely more authenticity than that moral system... denominated the natural law." Rather Wilson thought "[r]eason and conscience can do much; but still they stand in need of support and assistance," and that "the scriptures support, confirm, and corroborate, but do not supercede the operations of reason and the moral sense."