As I remember, Stephens said at the start of the war that the war was being fought over slavery. But after the war and upon further reflection, he said that that was too simple an answer, that slavery was the occasion of the war. The North and South differed greatly over philosophy of government right from the start and that this had led to many conflicts over the years, slavery being the latest. Of course, they also differed in more important things, like grits, but that wasn't quite enough to precipitate war.
IMO the war would not have come about at that point in time except for the slavery issue. The Morrill tariff might have also precipitated the rupture had it occurred earlier, but it passed after states had already seceded. As the New Orleans paper said about the tariff when it passed, "The South was to be fleeced that the North might be enriched." The paper fumed about sectional aggrandizement, which it felt was the policy of the Black Republicans.
Certainly the Constitutional issues and the sharp disagreements in the philosophy of government that Stephens mentions were discussed before the war. They were laid out on the floor of the Senate by Jefferson Davis.