I'm pleased that you are willing to ask questions. This was a big enough issue for Democrats that the party split over the issue of slavery in the territories. After a year or so of reading Alabama newspapers from the 1860 election campaign, it's clear to me that any other issue was a distant second.
The term "states rights" came about due to the position many Southern Democrats took on this issue, that all the states had a rights in territories under jurisdiction of the United States.
It's also apparent that most Southerners believed the Republican party to be a dangerous minority in the North. It was inconceivable that a majority in the North woud support the abolitionists. THat's why the election results came as such a shock.