Written after listening to too much of the Hamilton musical:
Alexander Hamilton doesn’t have an affair with Maria Reynolds for whatever reason. This also butterflies away his death in 1804. Over the course of Thomas Jefferson’s second term he becomes the main national figure for the Federalist Party, and thus the main figure in opposition to Jefferson. Hamilton runs in and wins the 1808 Presidential election as a Federalist, and proceeds to stay in office for the rest of his life. People of his time and social station were living for a pretty long time (John Adams made it to 90, Jefferson to 83, Ben Franklin to 84), so let’s say Hamilton lives until he’s 80, dying in 1835.
What do those 30 extra years of Alexander Hamilton, including 30 as President, mean for America?
Hamilton is much better for the army than the Democratic-Republicans he replaces. Rather than leave it underfunded and disorganized, he advocates for a strong national defense. If America still goes to war with Britain, either in the War of 1812 or some equivalent, it wins this time and conquers Canada and maybe even some of Britain’s possessions in the Caribbean.
Hamilton is also a lot better on the slavery question. He was an ardent abolitionist, while the Presidents he replaces were mostly slave owners. The big accomplishment here would be if Hamilton could reduce the spread of slavery. How about this: he manages to ban transporting slaves across state lines. So slavery remains legal in places where it had already spread – Kentucky, Tennessee, Alabama, Mississippi, but can’t grow that much in these areas because they can’t import slaves from the more established coastal states. Eventually the populations of these states can ban slavery for themselves, because they don’t have the same kind of incredible economic incentive to keep it as in places where slaves make up a large proportion of the population. Meanwhile, it also means that there is a lot more manumission in the existing slave states, as demand for slaves is lower, and thus there is less incentive to sell rather than free slaves. So the slave states on the Atlantic coast end up with large free black populations living alongside their slave populations, and the rest of the country develops larger than OTL free black populations as well when a lot of those freed leave home in an early version of the Great Migration.
Hamilton also sets up a much stronger national government, and centralizes a great deal of power in the Presidency. There is a lot more federal investment and economic management, and the country as a whole ends up more weighted towards the big cities and financial interests rather than the plantation class that dominated the economy in OTL.
On the other hand, Hamilton was not the most pro-democracy of people. He uses his control of the federal government to squash dissent and generally screw with his political enemies. He wins the elections of 1808, 1812, 1816, 1820, 1824, 1828, and 1832 by varying margins, and continues to face major opposition to his plans in Congress, but by the end of his Presidency it is almost inconceivable to many that anybody else could run the country.
This turns out to be true, and not in a way comforting to Hamilton’s supporters. He dies in 1835, and whoever his Vice-President is by that point takes over and wins the 1836 election with the help of the sympathy vote. The poor guy’s term in office doesn’t go that well, and the Democrats win the Presidency for the first time since 1804 in 1840, at the back of a populist wave. Hamilton had walked a delicate line between promoting the interests of capital, which he saw as key to the country’s power, and doing what he could for the people at large, who he of course needed to vote for him, and who he did have genuine compassion for. The rest of his party can’t walk this line. One faction is much more wedded to big money interests, and includes many people who joined up simply because it was the way to gain power. The other faction includes a lot of radicals, particularly a big abolitionist faction. When the Democrats take office there is a massive anti-corruption campaign in both the federal government and Wall Street, but they don’t manage to steer the country too much off the track Hamilton put it on (they didn’t even really manage that in OTL when they got to run the country for that whole period).
Interesting tidbit: ITTL George Washington is viewed as almost a puppet for Hamilton, who is seen as the Great Man of the revolutionary and post-revolutionary eras. Rather than getting less credit for his role in Washington’s many achievements than he should, Hamilton gets more, and Washington as a historical figure is a bit diminished.
Slavery peters out more gradually than IOTL. By the end of Hamilton’s Presidency a solid majority of states have banned slavery, and it is seen as an archaic institution. The vast cotton plantations of Alabama and Mississippi are worked by free labor. There are a lot of federal and state programs set up to buy and free slaves, and to encourage voluntary manumission. The slave free areas of the South don’t end up quite as full of independent yeoman farmers as the North does, since cotton does encourage economies of scale, but they are also far from OTL’s slavery-dominated nightmare. In the 1850s the first post-Hamilton Federalist (often called Hamiltonians ITTL) wins the Presidency on a reasonably strident anti-slavery platform, and manages to pass a law mandating that all children are born free. With this law in place, and no provision to actually enslave new people, the clock really starts ticking on slaveries continued viability. There are a lot more manumissions, and some slave states even begin to voluntarily ban the practice. By 1870 only 10% of the nation’s black population is enslaved, and in the early 1870s abolition finally becomes law nationally.
The American settlers who spearheaded Texan independence from Mexico were in large part driven by the desire to own slaves, which was illegal in Mexico. ITTL it’s clear that they won’t be able to have slaves as Americans either, so thing stay quieter. The US never takes over and territory from Mexico, which retains control of the sweep of territory from Texas to California. This territory gathers a similar population to OTL, including the Native American inhabitants, immigrants from the United States, internal migration from more populous areas of Mexico, and a huge amount of international immigration, particularly from Asia. This accelerates whenever they find gold in California. With this larger territory and without the devastating wars against the United States, Mexico does quite a bit better than IOTL. It manages to evolve into a reasonably stable democratic republic by the middle of the 1850s, and by 1900 is considered a developed nation.