Lincoln's biggest political mistake was the emancipation proclamation. He turned a war that was seen (rightly) by most people as a fight to preserve the union into a conflict over the slavery issue. Most people in the north and a minority but not insignificant number in the south were willing to fight and die to preserve the union, or to send their sons to do the same. Not many, no matter how repugnant they found slavery, would do the same.
I think you are overstating that. In 1864 the three year enlistments ran out. They Union army could have melted away to nothing, and I have to believe that if the majority of the troops thought the war was about slavery then a good part of it would have. Instead the overwhelming majority of the troops reenlisted, those who were fighting to preserve the Union reenlisted for that reason and those who were fighting to end slavery reenlisted for that reason. And the army remained and went on to defeat the Confederacy.
I've seen no evidence suggesting the Emancipation Proclamation was, net-net, a "mistake", much less "Lincoln's biggest political mistake".
Yes, into the fall of 1864 Lincoln expected to lose reelection, but not from Emancipation, rather from a string of Confederate Army victories, by Lee & Early in Virginia, Forrest in Mississippi, Kentucky & Tennessee, Taylor in Louisiana, Hoke in North Carolina, Johnston in Georgia and Shelby in Missouri, among others.
The news of Confederate Army victories did not begin to slack until September 1864 with Sherman in Georgia, Sheridan in Virginia and Blunt in Missouri -- enough to lift Union spirits and reelect Lincoln.
So how was the Emancipation a political "mistake"?
Did it elect more ant-war Democrats?
Did it delay the Confederates' Unconditional Surrender?
Did it reduce the size or fighting spirit of Union Armies?
I've never seen where it did, or seen it argued the Union would have been better off without the Emancipation Proclamation.