The abolition of slavery was not a serious issue in 1860 -- no reasonable person thought at the time it was even possible to do so and all recognized that the Constitution allowed slavery.
But the expansion of slavery into the territories was the major, and in fact the only issue in the election of 1860 and it was again acknowledged that the Federal government did have the Constitutional authority to forbid it.
Expansion not a new issue then. The issue of expansion had caused division, and even calls for secession all the way back to The Missouri Compromise of 1820 and again with Compromise of 1850.
With the passage of the Kansas-Nebraska Act followed by the Dred Scott decision in the 1850s, the sides were basically drawn in stone, and there was no longer any room for compromise. The Southern states demanded unlimited expansion of slavery and the North opposed any further expansion.
Lincoln ran of a 'Free Soil" platform and his only real promise was to stop the further expansion of slavery.
Further, the slave power also demanded that their rights to slaves extended to the northern states.
Previous cases had held that state officials of free states did not have to cooperate with slave catchers in the pursuit of accused run away slaves. Federal marshalls had that authority.
Dredd Scott decision expanded that, to deny any right an accused slave or person of African ancestry had to any consideration at any time. Dredd Scott was not a run away slave. He was knowingly taken to free territory and to free states by his putative master.