Not really, I think. Tariffs had steadily dropped since 1832, and while they were far from insignificant (~15%, give or take based on the specific products), they were far from huge, or even large. If they had been, the West would have joined the South in secession; the small-homestead populations of the Western population were just as ardently opposed to tariffs as the South, and for much the same reason. Compromise offers from both sides in the lead-up to the Civil War completely and universally ignored tariffs as an issue, and the resumption of high tariffs did not occur until after (a) the entire Southern wing seceded, leaving only a rump Congress, and (b) the war resulted in a drastic increase in federal expenses, necessitating new sources of revenue. While tariffs were a major issue even in 1832, people weren't willing to die over them even in the peak of the Nullification Crisis.
It is also telling that when one examines the issue far closer, not at the state level, but at the level of counties, that slavery becomes even more important of an issue. The Wheeling Convention was the most successful, but by no means the only counter-secession movement, and like the events that led to the creation of West Virginia, these movements are almost always geographically and economically tied to those regions of the South where slavery was at best weakly entrenched, such as in Appalachia; conversely, those who supported secession in the North were disproportionately from those regions where slavery held strong sway, such as Little Dixie in Missouri (though Missouri has certain particular circumstances during the war due to the ham-handed Unionist response to the Governor calling for secession). Indeed, it's also just as worthwhile to point out that there was actually a solid economic and cultural reason for poor white freedmen to support slavery, in a two-fold manner. First, the principle of the American Dream was that every man could make their fortune, and to these people, while they had no slaves at the moment, they could always bear the hope of making it big and buying a slave in the future as a sign of that wealth. Second, black slaves created an underclass that would be inferior to them, and thus implicitly improved their relative condition simply by existing. Ultimately, while I do not deny that there were those for whom it was a primary issue, "states' rights" was largely abused as a shield for the peculiar institution, and as mainiac has already pointed out, the South was just as willing to abrogate these rights whenever it benefited them and the defense of slavery.
And yes, there is a distinct trend to white-wash this. Yes, states' rights were an issue, but it was almost always and exclusively the right to have slaves. For fun, check out the state declarations of independence during this.
Mississippi is particularly telling, starting with a renunciation of the Ordinance of 1787 (most noteworthy for its renunciation of slavery north of the Ohio River) and the Missouri Compromise, goes to the Federal denial of protection to slavery on the high seas (the slave trade), refusal to allow new slave states in the Union, the effective nullification of the Fugitive Slave Law, "advocation of negro equality", fears of emancipation...it's basically a huge white-supremacy pact.