Stephens is speaking about a rejection of fundamental norms in a democratic polity, specifically that we use elections to decide who occupies the office and the winner wins. The loser must accept that. You can find lots of this rejection in the declarations of the causes of secession but those are the work of state legislatures, which are not candidates for office. The same holds for the speeches of secession commissioners.

With regard to presidential candidates, here's the thing: Presidential candidates at the time did not customarily campaign on their own behalf, but rather stayed home and referred people to published volumes of their speeches to get their opinions on things. Stephen Douglas campaigned anyway, partly under the excuse that he was visiting his mother and people just demanded he say something at every stop. But Douglas ran on a decidedly unionist platform. His appeal was largely that if the North voted for Lincoln, the South would really secede. When the war came, Lincoln showed Douglas his draft call for troops to suppress the rebellion and Douglas told him he should ask for more men.

So it's probably not Douglas. Nor would it likely be John Bell, of the Constitutional Union party. They were largely running as a compromise Unionist movement. That leaves us with Breckinridge, of the Southern Democrats. I'm not familiar with his rhetoric, but if he said something really astounding I suspect it would show up in the standard surveys.

It's possible that Stephens doesn't actually have a specific utterance in mind or his history in order. Referring to a specific thing to evoke a whole set of events is a common rhetorical device. Journalists and pundits doing bad history is pretty common too. Were he reading this, he might tell us that we're being insufferable pedants. We all know he's talking about the slaveholder's insurrection, the nation's most famous repudiation of democratic government.

That's fair, but looking for disgraceful statements from the early Civil War by people of presidential stature is always going to bring you back to Alexander Stephens, the Confederate Vice-President. He gave his Cornerstone Speech extemporaneously on March 21, 1861 at Savannah, Georgia. It's one of the canonical statements of Confederate ideology:

The new [confederate] constitution has put at rest, forever, all the agitating questions relating to our peculiar institution -- African slavery as it exists amongst us -- the proper status of the negro in our form of civilization. This was the immediate cause of the late rupture and present revolution. Jefferson in his forecast, had anticipated this, as the "rock upon which the old Union would split." He was right. What was conjecture with him, is now a realized fact. But whether he fully comprehended the great truth upon which that rock stood and stands, may be doubted. The prevailing ideas entertained by him and most of the leading statesmen at the time of the formation of the old constitution, were that the enslavement of the African was in violation of the laws of nature; that it was wrong in principle, socially, morally, and politically. It was an evil they knew not well how to deal with, but the general opinion of the men of that day was that, somehow or other in the order of Providence, the institution would be evanescent and pass away. This idea, though not incorporated in the constitution, was the prevailing idea at that time. The constitution, it is true, secured every essential guarantee to the institution while it should last, and hence no argument can be justly urged against the constitutional guarantees thus secured, because of the common sentiment of the day. Those ideas, however, were fundamentally wrong. They rested upon the assumption of the equality of races. This was an error. It was a sandy foundation, and the government built upon it fell when the "storm came and the wind blew."

Our new government is founded upon exactly the opposite idea; its foundations are laid, its corner- stone rests upon the great truth, that the negro is not equal to the white man; that slavery -- subordination to the superior race -- is his natural and normal condition. [Applause.] This, our new government, is the first, in the history of the world, based upon this great physical, philosophical, and moral truth.

This isn't what Bret Stephens said. Alexander Stephens was not a candidate for the presidency. Nor is his speech necessarily a repudiation of democratic norms as they were understood in 1861. (Or often thereafter.) Rather it's the events that led to him gaining the office he then held and put him on the stage that day which do that work. Those and the speech are pretty disgraceful, though.