I think these are things that are very difficult to disentangle. It's very difficult to talk about political or cultural strife in the 19th century US without emphasizing slavery. Sectionalism, while a valuable analytical concept, was to a great extent caused by slavery. There were aspects of North and South that differed apart from slavery, but the things people cared about broke apart on these lines. A lot of the sectionalism that amplified in the mid-19th century came about because of disputes about slavery. In a lot of the political arguments of this era, slavery is the elephant in the room so to speak. The white South grew increasingly nervous about anything that looked it could create room for expanded federal jurisdiction on slavery.

The tariff, honestly, ceased being a major issue by the end of the 1840s. There was still debate about it, but slavery had overtaken it as the dominant national issue. This largely had to do with the creation of new states in the Louisiana Purchase territories, and in the new territories conquered from Mexico. As long as there was a relatively stable political status quo in regards to the balance between slave states and free, there could be something an armistice, but what to do with newly acquired territories created new questions about this. So a lot of this was strictly political, free states didn't want to be overwhelmed by slave states, and slave states didn't want to be overwhelmed by free states.

To some extent, you can think of the relationship between slavery and sectionalism as a chicken and egg problem. As slavery became more and more divisive, institutions became more and more regionalized. White southerners increasingly encouraged their sons not to study at northern universities, and there were calls to foster independent southern literary and intellectual culture. National religious denominations, such as the Methodists, split over the issue. This, of course, is the classic setup for an echo chamber. Because southern nationalism and secessionism grew up in the context of the desire to defend slavery, it is hard to say that the South was just looking for a reason to leave.

I don't want my answer to be too long-winded, but there are additional details that underlie this, and I discuss some of them here in the context of a different, albeit related question.

Readings

James Mcpherson, Battle Cry of Freedom: The Civil War Era

Daniel Walker Howe, What Hath God Wrought: The Transformation of America, 1815 - 1848

William Freehling, Road to Disunion (2 vols)

James Oakes, The Ruling Race: A History of American Slaveholders

James Oakes, The Scorpion's Sting: Antislavery and the Coming of the Civil War