If the Confederacy had won at the Battle of Gettysburg

[Yellowhammer]

Public morale in the north would drop, and the civilians would possibly lose their appetite to keep sending their sons to die in a useless war of aggression.
Ideally a larger cohort of northerners would realize the need to rise up and get rid of the Lincoln regime, which was putting its power over the lives of the northern citizenry.

What the south should've done is not put all their eggs into the basket of conventional warfare, and instead flood Pennsylvania with bands of guerrilla fighters. Blaze a trail of destruction through the Union's heartland-- drive a steak through it's will to keep on fighting an illegitimate imperialistic war.