Depends on the exact circumstances.
Does the AotP nail all three southern corps? Does Longstreet escape? Can the Confederates reform south of the Potomoc before Richmond?
Assuming best case for the Union (85%+ of ANV bagged, plus Lee, plus Longstreet plus Stuart) the South is truly screwed. There isn't anything to stop the Union from simply walking into Richmond by early August. Coupled with Vicksburg, this is really bad.
The Confederate Government could flee, but it is difficult to see where it could go. Atlanta is the obvious choice, but so what? They set up shop and simply wait for the Union Army to make it there? They declare FESTUNG GEORGIA and go down swinging? It almost doesn't matter. The particulars are actually kind of irrelevent; the South is done.
Mike Turcotte