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.
The Union could afford to lose any of those four - or even all of those four (well, if there was a win at one of the earlier two for the CSA, there may not be a battle at the latter two) - and still keep going. The CSA, as Lee and Bragg found out OTL, could not simply shrug off a defeat there.
This isn't a balanced situation where a slight nudge could send it in favor of one side or another.
So, we're going to ignore the Western armies - which have been winning pretty consistently for more than a year now - why again?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).
No, it would not be fragile. Contrary to the delusions of McClellan, the Army of the Potomac did not represent the last hope of the Union.In the wake of yet another Confederate victory at Chancellorsville, Union morale would have been fragile by the time Lee invaded Pennsylvania.
Remnants?!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.
~80%+ of the Army of the Potomac is still intact, depending on the the figures one uses for it's starting strength (I'm using this:http://gburginfo.brinkster.net/unionorderofbattle.htm as my books are currently disorganized) even if you leave nothing of First and Eleventh Corps but ghosts, stragglers (including late arrivals like Stannard's brigade - around two thousand men, not counting the two regiments detached to watch the corps's trains, which brings it to three thousand), and prisoners of war.
"Lee owns the area south of town and Meade decides to pull back to Pipe Creek." is not a complete victory.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.
And it being militarily insignificant is precisely the problem. Sure, if Lee crushed the Army of the Potomac like Hannibal did to the Romans at Cannae, that would probably be rather demoralizing. But Lee is in no position to such enormous losses on the Army of the Potomac.
I am simply without words to describe the idea that because Davis believed something, it was self-evidently with foundation.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.