The Crittenden Compromise was one of the latest attempts to try and prevent the Civil War from happening. It was proposed by Sen. James Crittenden of Kentucky in 1860. The compromise proposed that all of the US should be divided at the 36 degrees 30 minutes line that the Missouri Compromise had set up. Any territory that was north of that line could not have slaves. Any territory south of that line could have slaves if it wanted. This would include any territory the US later got, such as Cuba.
This proposal was not accepted by Lincoln as he ran for election. He did so because he thought it would inevitably lead to wars meant to take territory for the slave states (in Mexico or even further south). By rejecting it, Lincoln rejected any real chance for compromise with the South.