Well let's have a look at the principles (taken from the Genocide):
The core political value of America is republicanism; citizens have a civic duty to aid the state and resist corruption, especially monarchism and aristocracy.
Not too different from OTL, but perhaps worse relations with Europe.
Jeffersonian values are best expressed through an organized political party. The Jeffersonian party was officially the "Republican Party" (although historians later called it the Democratic-Republican Party.
Not too difficult. Actually this may be the key to the problems people mentioned earlier. A stronger Jeffersonian tradition throughout politics, but with the rough edges and ideological awkwardness rubbed off by the party system.
It was the duty of citizens to vote, and the Jeffersonians invented many modern campaign techniques designed to get out the vote. Turnout indeed soared across the country.
This kind of thought might lead to, as in modern Australia, mandatory voting.
The Federalist Party, especially its leader Alexander Hamilton, was the arch-foe, because of its acceptance of aristocracy and British methods
How to nuetralize these jokers?
The yeoman farmer best exemplifies civic virtue and independence from corrupting city influences; government policy should be for his benefit. Financiers, bankers and industrialists make cities the 'cesspools of corruption', and should be avoided.
Low industrialisation is definately going to be a feature here. Might be interesting later when the US realizes it has to catch up. Personally I think this makes the scenario more, not less interesting.
The national government is a dangerous necessity to be instituted for the common benefit, protection, and security of the people, nation or community; it should be watched closely and circumscribed in its powers.
This thought is similar to what exists OTL, but more emphasized.
Separation of church and state is the best method to keep government free of religious disputes, and religion free from corruption by government.
Perhaps every time this American has a Great Awakening, the conflict between the religious and the government will see large groups of believers setting off into the frontier to set up little Protestant Deserets of their own. Conflicts with Indians would surely ensure, the Americans might supply the Indians with arms just out of spite. Sounds fun.
The federal government must not violate the rights of individuals. The Bill of Rights is a central theme.
Change of emphasis, what effects?
The federal government must not violate the rights of the states. The Kentucky and Virginia Resolutions of 1798 (written secretly by Jefferson and James Madison) proclaim these principles.
Slavery probably dies a natural death here, though it might hang out for a long time.
Freedom of speech and the press are the best methods to prevent tyranny over the people by their own government. The Federalists' violation of this freedom through the Alien and Sedition Acts of 1798 became a major issue.
How can this be encouraged at this early date?
The United States Constitution was written in order to ensure the freedom of the people. However, "no society can make a perpetual constitution or even a perpetual law. The earth belongs always to the living generation."
Not as bad as people think it is, and would probably help to ease some issues later regarding industrialization and such.
All men had the right to be informed, and thus, to have a say in the government. The protection and expansion of human liberty was one of the chief goals of the Jeffersonians. They also reformed their respective state systems of education. They believed that their citizens had a right to an education no matter their circumstance or status in life.
Free education in the States, perhaps? Interesting. That might end up extending to healthcare if the tradition continues. Bizarre from the perspective of OTL American politics, but a cultural distrust of government could probably co-exist with this.
The judiciary should be subservient to the elected branches and the Supreme Court should not have the power to strike down laws passed by Congress. The Jeffersonians lost this battle to Chief Justice John Marshall, a Federalist, who dominated the Court from 1801 to his death in 1835.
This might have unfortunate implications. Or maybe not. Maybe instead of Supreme Court decisions, referendums that are worked into the election cycle. Complicated, I guess.
The Jeffersonians also had a distinct foreign policy:
Americans had a duty to spread what Jefferson called the "Empire of Liberty" to the world, but should avoid "entangling alliances."
Sounds like lots and lots of rabble-rousing, more hostile relations to the Old World, maybe better relations with post-Independence Latin America?
Britain was the greatest threat, especially its monarchy, aristocracy, corruption, and business methods; the Jay Treaty of 1794 was much too favorable to Britain and thus threatened American values.
Britain as the Big Bad would be defining, I think. Maybe a cultural reflex to do the opposite of whatever Britain did?
France, at least in the early stages of the French Revolution, was the ideal European nation. Napoleon was the antithesis of republicanism and could not be supported.
More American support in the early days of the Revolution and things could be interesting. If the US survives, then further meddling in Europe would likely occur, particularly in Germany. Maybe the 48 revolution still fails, but more Germans come to America. Cultural dissonance occurs, but there is a solution: make more states just for them.
Louisiana and the Mississippi River were critical to American national interests. Control by Spain (a weak power) was tolerable; control by France was unacceptable. See Louisiana Purchase
If France was a pal it might not matter so much. Might even split the place.
A standing army and navy are dangerous to liberty and should be avoided; much better was to use economic coercion such as the embargo. The militia was adequate to defend the nation. But it proved inadequate in a major War of 1812 when miitia units refused to leave their state to attack the British.
This is a toughie. But there must be a way around it that holds to the core principles. An American Foreign Legion of liberty-seekers might be an interesting way to circumvent it (bring your family, serve for ten years and you're all citizens).