The correct option is "He and Jackson disagreed over the Nullification Crisis."
John Calhoun was a political leader of the southern states of the United States, a prominent political philosopher of the first half of the nineteenth century and one of the main actors in the great political disputes in his country. In these disputes he played an outstanding role as a spokesman and defender of slavery, of the nullity and of the electoral rights of the minorities of the upper social classes, especially of groups such as slave owners, over the majority of the lower social classes. . His ideas are considered vital for the future constitutional crisis that would end in the Civil War, a decade after his death.
John C. Calhoun served in several federal jobs (which he called "nationals"), as well as seventh vice president of the United States between 1828 and 1832, during the presidencies of John Quincy Adams and Andrew Jackson. He resigned from that position to be elected to the federal Senate, where he would exercise much more power and influence than as the president's second man. He also served as a representative before the respective Chamber between 1810 and 1817, as the tenth Secretary of War (1817-1824) and as the sixteenth Secretary of State in 1844 and 1845, under the presidency of John Tyler.