Radical reductionism, in one form or another, well antedates the verification theory of meaning explicitly so-called. Thus Locke and Hume held that every idea must either originate directly in sense experience or else be compounded of ideas thus originating; and taking a hint from Tooke we might rephrase this doctrine in semantical jargon by saying that a term, to be significant at all, must be either a name of a sense datum or a compound of such names or an abbreviation of such a compound. So stated, the doctrine remains ambiguous as between sense data as sensory events and sense data as sensory qualities; and it remains vague as to the admissible ways of compounding.
The leading lights of the American Revolution were well acquainted with David Hume's writings, especially his History of England. Although the young Jefferson at one point praised Hume as an Enlightenment figure, he gradually grew to detest Hume, who he viewed as “the great apostle of Toryism”. Hume's writings certainly influenced the political views of the Federalists as well. While Jefferson may have been friendly with Madison (though probably not until after the ratification of the Constitution), he was not sympathetic to Madison's ally Hamilton nor in agreement with the Toryish sentiments of the Federalist papers, which often resembles quotes from Hume's "Essays" ("Essays, Moral, Political, and Literary"). Hamilton and Madison echo Hume's anti-democratic sentiments--if not classical arrogance--in their concern for the potential danger of democracy based on consent.
Jefferson the Lockean democrat (democratic in principle--TJ even outscores Locke on the Hypocrisy-meter) had nothing but contempt for monarchy and aristocracies. The Federalists however were not convinced that the ideas of Locke or Algernon Sydney should serve as the basis of the new Republic; indeed, the Federalists paid little attention to the English Civil war, or Locke and Sydney's battles against Charles II (Sydney delivered a rather eloquent speech before Chas II's men decapitated him). The Federalists instead focused on their favorite latin and greek classics. Hamilton seems fonder of historians--Thucydides, especially--than of philosophers, but the trusty Stagirite (Aristotle) does appear fairly frequently in the Federalist papers (and in the writings of all Tories for that matter). Aristotle, while perhaps not a thorough-going totalitarian, was not a democrat, and generally argues for a type of aristocratic-republican government led by a few. He's the granddaddy of the Tories and royalists, including Hume (not to say the Roman Empire and Catholics, Inc...and much later, Nietzsche (sort of Aristotle's stoicism, sans Deus), and....Miss Ayn Rand).
Some scholars have however argued that Hume did not consistently uphold Tory or royalist values, and at times supported the Whigs, at least in principle.
""The Whig principle of consent as the basis for just government was, from Hume’s viewpoint, not so much philosophically false as practically dangerous. If Hume’s purpose in writing his essays had been simply theoretical, then his sceptical philosophy would have provided him with far more reason to attack the Tory divine-right doctrine than the principle of consent.
Hume would have granted that in the past the divine-right doctrine had been used to justify political and religious oppression. By his time, however, there was no longer any likelihood that it would become a widely accepted and politically dangerous doctrine. Hume would appear to have foreseen an increasing acceptance and radicalization of Whig principles, and his attack was aimed more at the propaganda of intemperate Whig spokesmen than at the Lockean principle of consent."""**
Hume reportedly did not care for Locke (either his empirical-realism or politics), and that may be a bit far fetched. The American framers, whether Federalist, or Anti-federalist, were preoccupied with the problem of consent, however--as were the french encyclopedists, and later the jacobins, who took Rousseau for their political mentor (Rousseau knew Hume, and Hume actually lent him money, but they eventually had a falling out as well). While Hume may have been a "sober decent libertine," according to Adams, Hume considered Rousseau a madman. Rousseau of course supported democracy, if not a type of egalitarian socialism, opposed the divine right of Kings in any form--as did Locke (Rousseau respects though does not worship Locke's writing on the social contract).
In effect the battle for the ratification of the Constitution waged between the Federalists and Anti-Federalists (led by that well-spoken virginia anti-Federalist RH Lee, great uncle of Robert E [RH favored abolition, however]--as well as Clinton, Mason, Henry, etc) appears like a showdown between Humeans and Lockeans. Jefferson was employed as the US Ambassador in France, though evidence suggests he favored the anti-Federalists; though not all the anti-Federalists admired Jefferson, who was considered an ally of the wretched jacobins--a point Adams hammered on in the campaigns of 1799. Hume did not live to witness the rise of Robespierre and the jacobins, but one suspects he would have been sympathetic to the Condorcet faction (and probably later to Burke).
Jefferson probably disliked Hume's cynicism and misanthropy as well:
It may seem strange to the modern mind that Hume would have thought it necessary to discredit noble principles or to teach opinions which are not simply true. Interpreters in the tradition of Jefferson would no doubt say that such actions reveal Hume’s low opinion of human capacities, but Hume would undoubtedly reply that such critics show a lack of discrimination in failing to distinguish between philosophic men and ordinary citizens. Most citizens are guided by opinions, and what is philosophically true might be a very dangerous political opinion.
Thus Hume opposes the Enlightenment belief that all political problems can be solved by making true principles accessible to all men. In a letter to Turgot, Hume politely objects to the French economist’s “agreeable and laudable, if not too sanguine hope, that human society is capable of perpetual progress towards perfection, that the increase of knowledge will still prove favorable to good government, and that since the discovery of printing we need no longer dread the usual returns of barbarism and ignorance. Pray, do not the late events in this country appear a little contrary to your system?”14 Hume’s own view is akin to the classical belief that political society must rest on “noble lies.” Madison appears to agree to this when he refers in the forty-ninth Federalist to the proposition that “all governments rest on opinion.”
Whether one cares for Hume's character or not, Hume's republican concepts (including the electoral college, arguably) form part of the foundation of the US Constitution.