Thank you, I couldn't recall the name of it.
If I may suggest so, have General Rosecrans killed by a Confederate sniper while attempting to rally his breaking right flank at the Battle of Stone's River. His Chief of Staff was already dead, so his death will throw the Army of the Cumberland into chaos at the worst possible moment; between the anvil of the river and the hammer that is the Army of Tennessee, Rosecran's force would be shattered with immense losses in an early version of Chickamauga. Coming on the heels of Fredericksburg, such a victory would likely strengthen the forces behind the motion and likely force the Union to lift the siege of Vicksburg in order to confront Bragg.
My TL's problem, though, is that my narrative objectives require that Vicksburg more or less happen as OTL. Because the Union's control of the Mississippi -- and the necessity of Mississippi to any viable Confederate state -- is the lever that's used to ratchet out a negotiated peace that can actually be sold to the Northern public prior to the 1864 election. As viable-but-massively-discontented Confederacy opens up all manner of more interesting storytelling possibilities than LULZ DIXIE STRONK.