Jonathan Rowe at "Positive Liberty" has a good post on John Witherspoon, in which he points to Roger Kimball's article on Witherspoon. I'm pleased to see that Kimball notes the importance of Hutcheson for Witherspoon's "Lectures of Moral Philosophy," and that he at least touches on the likely suggestion that Witherspoon's populism had perhaps as much to do with his Evangelical partisanship as his political philosophy. (The Evangelical Party of the Church of Scotland were also called the Popular Party because they believed that ministers should be elected by congregations; they opposed the Moderate Party, who argued for the patronage system. Around this core distinction there grew additional distinguishing features -- e.g., the Calvinism of the Evangelicals was more conservative and Puritan-like, while the Calvinism of the Moderates was more liberal and Anglican-like.) I'm also pleased to see he notes Witherspoon's hand in passing on Scottish common-sense realism to Princeton. As Rowe notes, Kimball reads too much into Madison's vague comments on religious matters; although, following Berns, I think he overestimates the degree to which Witherspoon is Lockean. It would be surprising if Witherspoon had never read Locke; but there's reason to think that Hutcheson was a far more serious influence.
Further, Witherspoon was a conservative participant in the Scottish Englightenment; like almost every major figure in the Scottish Enlightenment (the most important exceptions being Hume and Smith, who were only nominally Presbyterian), he was a Calvinist, and like every other Evangelical he was a very serious Calvinist. To make some of the claims Rowe makes in the discussion thread he links to, we would need to be able to make a sharp distinction between the basic principles of the Scottish Enlightenment and the way educated Calvinists of the Scottish Enlightenment understood Calvinism and the Bible. I see no evidence that we can do so, although it is a subject that needs more research. Witherspoon is not a 'mediator' between Enlightenment philosophers and Christian theology, because the Enlightenment he was acquainted with was not set over against Christian theology as something requiring such a mediation. This seems typical of most of the major Presbyterians of the Scottish Enlightenment -- Reid, Campbell, Beattie, and the like. If 'mediation' just means that they can carry both labels, that's right; but the fact that there are two labels doesn't mean that there is any sharp division between the two. One is a loose set of family resemblances among thinkers geographically and chronologically linked; the other is a living tradition. Since the labels are of completely different sorts, it doesn't seem possible to distinguish principles as Scottish Enlightenment principles rather than principles of eighteenth-century Scottish Calvinism.
Of course, Rowe is right that none of this implies that the Declaration of Independence, or anything that followed is intrinsically Calvinist; only that it is all such that a Witherspoon, i.e., well-educated conservative Calvinist from Scotland, could enthusiastically support it.