That's simply inaccurate. There was a third choice - or what should have been the slaveocracy's first choice - maintain the status quo. Lincoln said that his wish was to keep the union intact - with or without slavery. He was willing to suspend his own views, and the views of the abolitionists if that was what it took to keep us together.
Maintaining the status quo would mean that they could continue to own other humans and use them as chattel with only a minor irritant coming from those pesky abolitionists. They could continue to hold a prominent position in Congress and likely regain the white house.
Life could have remained good, at least for the slavemasters, and at least for a while. But the fire-eaters knew that the world was evolving and that they would not be able to hold the water back for much longer.
The War of Southern Aggression was their last gasp effort to impose their worldview on the rest of the nation. Didn't work out too well, did it?
No, particularly since Lincoln's actions nullified the Compact.
§ 203. The treaty is void by the destruction of one of the contracting powers …….Thus, when a state is destroyed and the people are dispersed, or when they are subdued by a conqueror, all their alliances and treaties fall to the ground with the public power that had contracted them.
Book II, Chapter VIII, Law of Nations
Congratulations, you won, and your reward is an unlimited government.