Southern interests had more-or-less controlled the federal government since its inception. Southerners had occupied occupied the Presidency more than Northerners; they had more Justices of the Supreme Court and more Chief Justices; they had a long-time voting advantage in the Senate; and their interests were well-represented in foreign policy.
However, the political re-alignment of the 1850s and 60s, first with the destruction of the Whig Party, and then with the southern revolt in the Democratic Party before the election of 1860 (then, the only national political institution left), put the South into a decided minority status. The demographic trends had already put Republicans in power in the House, and the southern ruling coalition in the Senate was crumbling.
We have seen the histrionics from the Democrats in the last couple of elections - magnify that by about 100 fold, and you'll get an idea how the south reacted to Lincoln's election as President.
Exactly right, as Jeff Davis stated, the South was afraid that the millions of dollars they had tied up in slavery would disappear if slavery was limited.