In the election of 1860, Democrats split 3 ways, running 2 pro slavery candidates and 1 that was neutral as to slavery, against the Republican Lincoln who also had a ambivalent position on slavery, opening saying he'd do whatever it took to preserve the Union, including preserving slavery if that's what it too, yet his running mate was an abolitionist.
Bell was the Constitutional Union party candidate, who took a neutral position on slavery. That party was a split off from the Democrat Party
Breckinridge was the Southern Democrat Party candidate, who wanted slavery even more than Douglas
Douglas was the Democrat Party candidate who wanted slavery, even saying blacks were subhuman, not the same species.
Breckinridge won the most electoral votes, Douglas the most popular votes. Among the Democrats.
Lincoln won the electoral votes with a majority, but only a plurality of the popular votes, edging out Douglas. Lincoln won less than 40% of the popular vote.
Democrats were seemingly "united" in support of slavery, if you count the neutrality of Bell as a weak neutrality. But split 3 ways in a way that ended slavery in the end. Republicans were a minor 3rd party until 1860. Democrats seemingly didn't notice their intra party disputes and splits would end the very slavery they wanted. President James Buchanan approved the Breckinridge split for Southern Democrats. When the titular major head of the Democrat party approves a major split in the party, it's hardly "united." It was all similar to Teddy Roosevelt starting the Progressive Party, splitting Republicans so Woodrow Wilson the Democrat could win. Or Ross Perot splitting the Republican Party so Bill Clinton could win.