Sectionalism between the North and South was growing during Jackson's presidency, and the notion of States' Rights came into specific focus and popularlity during that time. Not that it was a new idea, but there was more of an urgency to it, both in the Tarriff of "Abominations" argument between himself and Vice President John C. Calhoun and the South's growing nervousness about protecting slavery as an institution.
Neither of the previous answers deals with the issue presented by the Bank of the United States nor the problem of the Indians which Jackson faced. For his own personal reasons, Jackson considered the BUS a monster, and was determined to destroy it. He once commented to Martin Van Buren,
the bank, Mr. Van Buren, is trying to destroy me; but I will destroy it."
Ultimately, he vetoed the bill for the renewal of the bank and also withdrew all federal funds from the bank, thereby destroying it.
He also of course, ignored John Marshall's decision in Cherokee Nation vs. Georgia and forced the removal of the Cherokee Indians to Oklahoma.
Both these issues demonstrate Jackson's determination to impose his will on the nation.
In Jackson's mind, one of the major problems was the problem of how to protect the common people from the machinations of the rich elites. Jackson felt, for example, that the Bank of the United States was a mechanism used by elites to dominate the economy and hurt the common people. Jackson felt that this was a major problem, which is why he fought so hard to destroy the bank.
Like all new Presidencies, Jackson faced some significant challenges in his new administration. I think that one of the most significant challenges had to have been how Jackson was going to grapple with the economic reality in which the nation was approaching the mid 19th Century. Jackson understood that the need to ensure economic progress was vitally important. This caused him to enact high tariffs on goods coming into the United States as a way to develop revenue streams that he was able to use to pay down the national debt. Yet, an offshoot of this was the Nullification Crisis, in that Southern states, particularly Jackson's Vice President's, John C. Calhoun's, home state of South Carolina, could nullify the President's tariffs. Not only was this a challenge internally between President and Vice President, but the need to use troops to put down the rebellious tone of the states, something that would become another critical issue in the midpoint of the century with the Civil War. Jackson was one of the first presidents to have to wrestle with the idea of state rights being seen as a manner to break with the federal government.