I prefer later Civil Wars myself (I've done two already, one beginning in 1868 and the other in 1879.)
There was a discussion on here about the Nullification Crisis turning into a Civil War. Not necessarily just about Tariffs, but having William Wilburforce tour the Union to campaign against slavery and hopefully get some material for his fight in Parliament.
This stirs up abolitionist sentiment earlier in the United States. The Nat Turner Rebellion throws Virginia into the states' rights loop and Nullification of the Tariff is soon coupled with a law that the northern states are trying to push through: one that is basically defined as an anti-slave capture law. If a slave ends to a free state, he is no longer a slave. It brings up Fifth Amendment issues, but John Marshall doesn't waver on his decision. The law stays in place and the southern states each nullify the bill one by one in their own state legislatures, beginning with South Carolina, Georgia, and soon Virginia. Virginia's the important state, leading the south in the war. When the Force Bill passes through Congress, secession would most likely immediately follow.
Victory for the south would be, if not assured, much more likely. They have a more even population in the 1830s, an equal economy, and aren't overpowered by the amount of Union states.
Of course, assuming it's 1833, the CSA (again, just for the sake of argument, calling it the CSA) would consist of Virginia, North Carolina, South Carolina, Georgia, Alabama, Misissippi, and Louisiana. Most likely Arkansas Territory too.
Tennessee and Missouri are the toss ups. Kentucky to some degree as well. I believe Missouri was a lot more southern in the 30s than it was by the 60s, keeping it in the Union by then. This early on... they might secede. Tennessee is Jackson's home and I find it kind of hard to believe they'd up and abandon the President like such. They're pretty Unionist there too. As for Kentucky? It'd be interesting to see Tennessee stay Union, and Kentucky secede. A very interesting war indeed.