What if General Lee re-deploys?

Probably been asked before, but what might've happened had General Lee chose to redeploy his forces south of Gettysburg to advance on Washington DC instead engaging in pitched battle as per OTL?
 
First off, getting around the Army of the Potomac isn't that simple a task. If he disengages Day 1 at Gettysburg, there's still substantial portions of the Union army well south of Gettysburg marching up the same roads he will want to use. If he attempts to slip around the Army of the Potomac after it fully concentrates at Gettysburg, he likely has spent a substantial amount of his ammunition by this point. If he magically manages to slip around the Army of the Potomac and march all the way to Washington, he's leaving a gigantic well supplied army in his rear in service to bashing his army against heavily manned fixed defenses at D.C. And he's doing so on a much tighter logistical budget than either the defenders at Washington will have or the Army of the Potomac behind him will have.

Lee had some amazing tactical victories and he took great risks at times, but this would have to be a masterpiece to end up being a successful gambit. If the DC defenses delay him almost any time at all, the Army of the Potomac sandwiches him in and forces him to withdraw or traps him there. Lee can't afford to be trapped very long. If Lee were to attempt to maneuver around the Army of the Potomac, his best move would be to do so in a manner that afforded him the chance to defend ground of his choosing against Meade in hot pursuit preferably much farther north than DC and in a place that affords him the opportunity to easily withdraw across the Potomac River after the conclusion of the battle. He most likely cannot take DC without shattering the Army of the Potomac decisively(highly improbable) and getting substantially resupplied and reinforced afterwards(pretty questionable).
 
Longstreet’s proposal was rather vague in many respects. It was supposedly a sweep of many miles, necessitating a change of base for the Army of Northern Virginia. The plan made good sense in abstract, but was utterly impractical to execute.

Firstly, Lee does not even have a direct road south from Gettysburg, the southernmost road (Emmitsburg and Taneytown) were in Union hands. The best road available in Lee’s situation is the Fairfield road, which leads the AoNV southwest and is in plain sight of Buford’s cavalry division. In addition, Meade has the southernmost road, increasing the chances of Meade beating Lee to the south.

Secondly, the cavalry brigades with Stuart have yet to return. Although Stuart left a few cavalry brigades with Lee, these cavalry brigades were used to cover the flank and rear of Lee’s army and Jenkins’ brigade (the cavalry brigade brought to Gettysburg) was inexperienced in conducting reconnaissance. Lee needs Stuart back to screen and scout for the offensive movement.

Thirdly, it’s the dreaded L word, logistics. Lee would need to adress his supply lines and reroute his supplies. Planning for such a matter would take an entire day, let alone actually executing the task. OTL it took 24 hours for the first wagon to get out of Gettysburg after Pickett’s charge on July 3rd.

Supposing that Lee ignored all of these issues and attempted it, Meade would realize that something is up. Meade is already advantaged by the fact that he has already posted cavalry brigades to watch his left flank for any Confederate movement. By the time any Confederate offensive kicks off, Meade has already concentrated his army and is prepared for any moves by Lee. The result of Longstreet’s proposal depends on what happens next, but I think it’s safe to say that it won’t be much better to Lee’s decision to attack on July 2nd.
 
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