Lincoln and the Republicans rejected John Crittenden's proposal to save the nation from southern secession because it called for the expansion of slavery into new western territories.
The Crittenden Compromise, proposed in December of 1860, called for the extension of the 36'30 line created in the Missouri Compromise. Instead of having this line end at Missouri, Crittenden wanted to expand it all the way across the US. This would mean any territory or state south of this line would allow slavery. Any territory or state north of this line would outlaw slavery. Republicans disliked this idea, as there goal was to stop slavery from spreading into any new state/territory.