My first thought upon seeing Jackson facing civil war was "What? Already?" Abraham Lincoln, whose presidency is defined by the Civil War, is still 9 presidents away. But the small-c, small-w civil war that loomed over Jackson did not have at its core the familiar issue of slavery---it concerned the Nullification Crisis, a huge deal that history largely has forgotten (at least it was never taught to me).
Basically South Carolina passed a law that declared the Tariff Act of 1828 (passed by Jackson's enemy and predecessor, JQA) unconstitutional, and inapplicable to its citizens. This was indeed a crisis. Though the Constitution created a federal government of limited and enumerated powers, its power to tax had never been questioned. If the citizens of South Carolina were exempt from paying federal taxes, all United States citizens would also be, and the union would dissolve. Similarly, if any one state were to have the power to declare federal laws unconstitutional, no federal law could ever be enforced.
Many South Carolinans and interested observers expected some support for Nullification from the new President Jackson. He was swept into office with a populist states' rights message. Surely he would support a state's ability to disencumber itself from the tax-happy feds. However, and after a good amount of dithering, Jackson stated certainly: "I consider, then, the power to annul a law of the United States, assembled by one state, incompatible with the existence of the union, contradicted expressly by the letter of the Constitution, unauthorized by its spirit, inconsistent with every principle on which it was founded, and destructive of the great object for which it was formed." Jackon's Vice-President, John Calhoun, disagreed and left his post to become a South Carolina senator.
Both sides began gearing up for conflict. Jackson made absolutely clear that he would not hesitate to send troops to South Carolina to enforce the tariff, and Congress passed the Force Bill, allowing him to do just that. On the brink of war, Henry Clay, the Great Compromiser, reached a solution that all parties agreed with. Basically South Carolina would pay its taxes, and the tariffs would decrease each year for a period of nine years. War was averted.
Yet it would be folly to dismiss the Nullification Crisis as an isolated incident---the basic battle lines that it drew were apparent in the Civil War, and persist today. You had on one side the strong federal government people, who believed in laws that were more or less uniform- each state was an equal member of the union, and had to be taxed as such. On the other side was the state's rights contingent, who believed in a "weak, inactive, and frugal federal government."-- states should be allowed to do almost whatever they wanted including interpreting the Constitution and allowing slavery. From the Crisis forward, "states rights" became euphemistic for "allowing slavery," and every state who supported nullification ended up seceding from the union during the Civil War.
This division exists today, evidenced by Rick Perry's threat that Texas secede from America to protest the President's stimulus packages, and the Tea Partiers allying themselves historically with those who believed they should be free from unjust national taxes. The Nullification Crisis should perhaps teach us that such rhetorical protesting can have dramatic real-world consequences. In the run-up to the Civil War, only one state decided to secede without dramatic disagreement and in-fighting. That state was South Carolina, which had already been waiting 25 years for its opportunity.