Hello,
Interesting question, let me follow the logic. The Republican Party nominated Lincoln as their candidate. A free and fair election was held and Lincoln won, he's president. However, the Confederacy is angry that he won so you suggest Lincoln should resign? Who then would take his place? Another Republican (Seward?), a Democrat (Douglas, Breckinridge, Bell, etc.), or a member of the Confederacy (Jeff Davis, Alex Stephens)? What is the alternative you suggest? Why is it preferable to honoring the results of a free and fair election?
Best,
Sam.