Yes, Kansas-Nebraska, and then Dred Scott IIRC, took down the Missouri Compromise -- but the contentiousness of the debates, and most of all the deep divisions in long-term interests between the industrializing North and the agrarian South and West that they illuminated, are what did the damage and convinced a lot of Southerners that North and South were, in fact, two countries united by historical happenstance, but not by interest and inclination.
As for the tariff, it might have come down under the political influence of the National Democracy, but it didn't take a rocket scientist to see that the rates would go back up whenever the Northern States, because of their immigration rates (helped differentially by all the cholera and yellowjack down south), finally got the legislative advantage over the Southerners and introduced them to 200 Years of Hell.
There was no shortage of bad feeling around the country by then -- as witness the affair of Senator Sumner's speech, followed shortly by Rep. Preston Brooks's pointed objection.