Both Hamilton and Jefferson had very contrary views of how the early republic's government should be established. In fact, they were the foremost advocates of their points of view in the scene of national politics, meaning that they were each considered the fathers of Federalism and Republicanism, respectively.

Hamilton believed the role of the government, and especially the federal government, should be strong. He did not think it was in the interest of the American people to have a national government limited by the rights of states and individuals. Hamilton was famous for his preference for a very strong executive branch of the government, going so far as to recommend an executive for life during the drafting of the Constitution—effectively giving America a king right after they had won freedom from England's King George III. He also envisioned America as an economic power, one of the few men with the vision to build a modern economy, but realized that it needed huge amounts of capital to make this happen. This is why his greatest achievement was building the national bank, ballooning the Department of the Treasury to create a national institution that could lend money, finance growth, and pay down its debts.

Jefferson, by contrast, believed that the national government should not be more powerful than the state government. Jefferson, like many other Founding Fathers, considered himself a Virginian before he considered himself an American. He believed limited, local government functioned best. In this manner, it is very ironic that his arguably greatest act as president was, in fact, a tremendous display of national authority: the Louisiana Purchase. Jefferson's view of economics reflected his background as an aristocratic planter with debts; he disliked the idea of the national government issuing money and financing perpetual debt. He argued against the creation of a national bank, both in the newspapers and in the cabinet of George Washington.

Alexander Hamilton believed in a strong central government and weak state governments. Hamilton believed that a national bank funded partially by tariffs would not only tie the states to the Union, but also protect factory owners in the early Republic. Hamilton thought that the United States's future lay in producing factory goods. Hamilton also believed that a strong national military was the best way to keep the new nation safe.

Thomas Jefferson, on the other hand, believed that the new nation should have a weak central government and strong state governments since the state governments would be more responsive to the people. Jefferson thought that a national bank would centralize power in the hands of a few elites. Even though Jefferson was one of the biggest slaveowners in Virginia, he believed that the nation's economy should be agricultural, since the small yeoman farmer had more at stake in terms of taxation. Jefferson viewed land ownership as the ideal goal for most Americans. Since Jefferson believed in a weak central government, he thought that a national military would be a tool used by a tyrant and that the nation should promote its state militias. This attitude toward cutting military funding would prove to be disastrous under the presidency of Jefferson's successor, James Madison, during the War of 1812.

Hamilton, who was George Washington's Secretary of the Treasury, argued for a powerful, centralized state. He wanted a standing army, a national bank, assumption of state debts by the federal government, and high protective tariffs. These measures and institutions reflect the fact that Hamilton envisioned an economy based on manufacturing, one which would allow the United States to rival Great Britain, the nation which Hamilton's economic system fairly explicitly emulated. Jefferson, on the other hand, thought these measures were anathema to a republic of free people. He envisioned an economy and a society based on landholding farmers, whose produce would allow the United States to achieve and maintain economic independence. Rather than producing manufactured goods, which he thought would produce a large, propertyless working class, Jefferson proposed that the new nation should simply trade for many of these goods. Accordingly, he favored a fairly weak central government, one which kept most of the powers of governing at the state level. Perennially in debt himself, he had a visceral distaste for such financial institutions as the proposed Bank of the United States, which he thought unconstitutional in the first place. 

The disagreements between these two men and their followers, which also involved foreign policy, contributed to the development of the Federalists and Republicans, the nation's first two political parties. Many of these issues, particularly the proper scope and extent of federal power, are still current today.