This explains why Britain was crushed by the American victory at Montreal.
Oh wait.
Or, to pick an ACW battle, why everyone remembers Munfordville.
. . . does anyone remember Munfordville?
People drastically underestimate Union morale when thinking that the Union will be shaken to its foundations just because the Army of the Potomac lost a battle north of the Potomac.
Munfordville was not a major battle on the scale of Perryville, Murfreesboro, Antietam, or Gettysburg, with the outcome in doubt, and the future of the Union and the Confederacy on the line. If it was, we would have remembered it, regardless of who might have won it.
A Confederate win on July 1, 1863 including the subsequent takeover of Cemetery Hill and Culp's Hill would have sufficed, considering two entire Corps of the Army of the Potomac had been virtually destroyed.
And I think you overestimate northern morale. Remember that throughout the previous two years since the war began at First Manassas, the Union had not had a single major victory over the Army of Northern Virginia worthy of the name (Antietam was basically a draw, that turned technically into a 'victory' upon Lee's subsequent withdrawal). In the wake of yet another Confederate victory at Chancellorsville, Union morale would have been fragile by the time Lee invaded Pennsylvania. Another victory by Lee on July 1, combined with the destruction of two entire Corps of the Army of the Potomac, and the retreat of the remnants of the northern army on northern soil before victorious invaders -the news headlines would have been unforgiving before a war-weary northern readership. And then there's the panic factor setting in, with widespread fears that Lee could strike Baltimore, Philadelphia, or even New York before besieging Washington.
Lee's ultimate intention was to break the will of the North to continue the war. If he had won a complete victory at Gettysburg on the First Day, that mission would have been accomplished, say what you will of its military significance. That is why President Davis had sent a peace envoy along with terms of surrender to Washington. The South could never militarily defeat the North, but psychologically? They came damn close in OTL.