Jackson and Calhoun had a very rocky relationship. The tariff and nullification issue was but one part of that poor relationship.
Calhoun and Jackson were very different people to begin with. Calhoun was not born in the highest class of South Carolina, but he was well-off enough to attend law school at Yale. Jackson, meanwhile, is famous for his lower-class background.
Even with this difference in background, the two seemed to work relatively well together until the tariff issue exploded. Calhoun supported nullification while Jackson believed in the need for the federal government to have supremacy. Their public differences on this issue really ruined their relationship.
Later, other issues made things even worse. There was the “Petticoat War” over Peggy Eaton and whether she was to be tolerated by Washington society. Calhoun’s wife was one of the main anti-Eaton leaders and Jackson took that personally. It was also revealed that Calhoun had favored censuring Jackson for his actions in an Indian war in Florida in the 1810s. These other issues further ruined the relationship between the two men.
Jackson and Calhoun, then, ended up fiercely opposed to one another. This was due in large part to their differences over nullification.