What event cause the eventual split of the democratic party, paving the way for the republican party and abraham lincoln?

The Democrats of the South defended the institution of black slavery, and most of the Democrats of the North did not dare to oppose their comrades from the South, although not all shared that ideology; the anti-slavery Democrats were unhappy with their party (and many would end up moving to the Republican Party starting in 1854).

At the end of the government of President James Buchanan (1857-1861) the Democratic Party was in crisis; many important Democrats of the North had broken with Buchanan because of their excessive inclination to southern interests, and the Democrats of the South were becoming increasingly intransigent.

At the Democratic National Convention of 1860 the differences became insurmountable, and the break inevitable. The delegations of several southern states withdrew from the Convention when it did not approve the inclusion of a measure in favor of slavery in the party's Electoral Platform; and subsequently the rest of the Southern Democrats also withdrew from the Convention.  

With only the representatives of the states of the North, the Democratic Convention appointed Stephen A. Douglas as the Democratic Party's presidential candidate; but the Southern Democrats reacted by appointing another presidential candidate, who was none other than the Vice President of the United States at the time: John C. Breckinridge. The party went with two different candidates to the presidential elections, facilitating the victory of the republican candidate Abraham Lincoln.

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