What if, instead of forming a political alliance with the Democrats in 1864, Lincoln decides to placate the radical wing of his party by running with a Radical Republican as his VP? I'd assume he still wins the election with the support gained after Sherman takes Atlanta and the overall support of the Army vote. However, I think there are a few questions that then have to be answered:
1. Who is Lincoln's VP? I'd say Fremont is most likely as he was the electoral candidate of the radical wing IOTL and thus would be Lincoln's number 1 pick to unify his party. Both Sumner and Stevens IMO are too valuable in the Senate/House.
2. Is Lincoln still assassinated, or does a more hardline replacement disincentive Booth and other terrorists? If he is killed, when?
3. How does Reconstruction proceed? How is future American history impacted?