Remember that during the Washington administration, the United States was still an untested polity. It had only recently made the transition from a colonial entity to independent self-government. One of Hamilton's main goals was to establish a strong financial and economic foundation for the United States. To achieve this goal, he supported increased centralization of government and federal power.
As part of this larger program, Hamilton called on the federal government to assume the debts of the individual states. For one thing, Hamilton argued that the creation of a national debt ought to be understood as a net positive, in that it would tie creditors and speculators more closely with the federal government and the United States, making them personally invested in its success. In addition, Hamilton called for the creation of a national bank, to encourage lending and borrowing, and to more effectively coordinate the national economy of the United States. Finally, in order to support this increased fiscal spending on the part of the federal government, he called on increased taxation, specifically a tax on whiskey, in order to pay for this expenditure.
These measures were extremely controversial in Hamilton's time: indeed, his whiskey tax spurred an armed revolt against the federal government, called the Whiskey Rebellion. In addition, his vision of increased federal power was criticized by those who preferred a more decentralized system of government. Consider how his opponents charged the national bank with being unconstitutional. His economic program was highly controversial but critical in shaping economic growth in the early history of the United States.