I've read many Southern editorials printed in 1860. Breckenridge, Lane and other Southern Rights Democrats (as they were called) always denied any advocacy of secession. Opponents accused them of being in favor of leaving the Union if defeated. In 1860 no legitimate political candidate wanted to be associated with secession. In Alabama SR Democrats strongly denied secession as their aim. Breckenridge's opponents used the term 'secessionist' like liberals use the term racist today.
Let me assure you, a debate over secession was not what split the Democratic Party in 1860.