One obstacle that Andrew Jackson faced while in office was a political one. The Whig Party emerged in the wake of Jackson's veto of the Bank of the United States in 1833. They gained control of Congress and attempted to weaken the President, voting to officially censure the President for his veto and opposing most of his policies. For that matter, the National Bank itself had been, from Jackson's perspective, a major obstacle, an instrument of privilege and corruption sanctioned by a government that Jackson hoped to make more responsive to the will of the "common man" that made up a significant part of his political base.
Another obstacle was the Supreme Court under John Marshall. Removal of Native Americans from the Southeastern states was a major policy goal of Jackson's, and when the Marshall Court ruled that his Indian Removal Act was unconstitutional in Worcester v. Georgia, Jackson was faced with a major problem. He resolved this problem by simply ignoring the ruling, allegedly declaring that "Marshall had made his decision. Now let him enforce it." Indian removal, including that of the Cherokee nation that was party to the case, continued despite the ruling.
Finally, another obstacle was the emerging states rights movement in South Carolina. This movement came to the forefront in response to higher national tariffs that Southerners deemed destructive to their interests. Led by John C. Calhoun (Jackson's own Vice President) South Carolina formed a convention that claimed the power to "nullify" the tariff, and threatened secession if that right was not honored. Jackson, who favored low tariffs, nevertheless took a firm stand against the nullifers in 1833, urging Congress to pass a "force bill" that would allow the use of force to enforce the law. But Henry Clay in Congress also secured passage of a compromise tariff that resolved the states rights crisis, if only temporarily.