But I would assume most pulled their "right of revolution" from Locke and other Enlightenment writings (even the DOI) to support their decision to leave the Union.
John Locke's political philosophy is indeed featured heavily in the DOI, a political philosophy derived directly from his epistemology. And though it was Thomas Hobbes who was the founder of liberalism, it was Locke who introduced to modernity the right of revolution, a new form of legitimacy.
At least in the abstract, it was certainly a tricky idea because once you give common people a right to rebellion and the capacity to make legitimate revolution, it renders any government somewhat uncertain. See the French Revolution, I guess. But it seems America struck a decent balance.
But what I find interesting—and something that often gets overlooked—
Before Locke wrote the "Second Treatise," he wrote the constitution of South Carolina in 1669. And in that, he included slavery. He had a hierarchy of statuses. He either did not have the idea of social contract, or he simply did not express it in the SC constitution.
Of course, this was before the American Revolution, but it's kind of interesting.
Locke's influence on America, then, was not only theoretical but practical—if in a paradoxical way— as seen in the DOI on the one hand and SC's 1669 constitution on the other.