Let's say by some fluke, Lincoln loses in 1864. I'm thinking a combination of the Fremont-Cochrane Radical Democracy party managing to gain some momentum and spoiling Lincoln plus something else (A Brazilian entry into the war following the Bahia incident?) tips things to McClellan.
Now, OTL the war ended in May 1865. McClellan won't even take office until March 1865. I'm thinking Lincoln and decides to speed up the war effort and the war ends just as McClellan is taking office.
McClellan is thus the one presiding over reconstruction, with a House and Senate that are Republican-dominated. How does that go?