After the divinely appointed King Charles I was executed, England moved from a more absolute monarchy to constitutional monarchy. The colonists moved things here from constitutional monarchy to constitutional republic. Yes, in one sense it was a radical change; though given where the Monarchy in England stands today, part of a historical trend. Theory usually follows action. No doubt writers like Sidney helped provide a framework of explanation.
The point of departure in this discussion was natural law. My point is that appeal to natural law doesn't answer the citizenship debate. Birthers think it does, assuming a biological sense to that term (the "it takes two cats to make a cat" notion). But as I've shown, Lord Coke's opinion in Calvin's Case was predicated on natural law.
So, yes, the Framers recognized natural law. But saying that doesn't answer the debate.
Calvin’s Case - The Selected Writings and Speeches of Sir Edward Coke
http://oll.libertyfund.org/titles/911#lf0462-01_mnt034
3. There be regulary (unlesse it be in special cases) three incidents to a subject born.
1. That the parents be under the actual obedience of the king.
2. That the place of his birth be within the king’s dominion.
3. the time of his birth is chiefly to be considered; for he cannot be a subject born of one kingdom, that was born under the ligeance of a king of another kingdom, albeit afterwards one kingdom descend to the king of the other.
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Sovereignty cannot supplant sovereignty, so unless the alien formally renounces his natural allegiance, he's still an alien.....according to Lord Coke.