reposting because I botched the title In 1834, under President Andrew Jackson, the national debt was at $4,760,082.08. The next year it was at $33,733.05. How was such a drastic amount paid off?
Andrew Jackson sold off a lot of Federal land in the Midwest to private developers. The ensuing revenues were used to pay down the debt, while at the same time he also forcefully blocked spending. As far as Jackson was concerned, national debt was a bad thing and something to be dealt with at all cost.
That cost came in the form of a collapsing real estate bubble and an economic recession in 1837 after his successor, Martin Van Buren, took office. Jackson's dismantling of the National Bank and delegation of monetary power to the states resulted in a situation where the states took on debt in anticipation of future tax revenues and due to the bubble were unable to pay the debt and thus defaulted. The lack of government intervention to deal with the recession (i.e. via government spending) also contributed to the crisis as diminished private sector spending was not supplemented by government spending, starting a death spiral as private enterprises started a race to the bottom in prices. Essentially, the cycle worked something like this:
I am a company in textiles manufacturing. Suddenly demand for textiles fall. I have to cut my prices. To sustain this cut in prices, I have to reduce my costs, so I lay off workers. Now more people don't have any income, so they cut their demand for goods (or alternatively, people who DO have money are scared of the price crash and are hiding their money under their matresses). Now demand for goods has fallen more, I have to cut my prices again, and the cycle continues.
Ideally, the government would intervene at some point in this cycle in order to stop it, such as by acting as external demand (acting as a buyer). This however costs money, money that the government didn't have (due to diminishing tax returns) and would result in deficit spending, which is what ended up happening anyways over the following years.