I think if Meade had attacked on July 3 or 4 on the Gettysburg battlefield itself, the Confederates probably would have held their ground and gotten some back for the beating they had just received. As already pointed out, despite having won the victory, the Union army was in a shambles, having suffered enormous casualties and lost many of its best commanders. It was probably wise of Meade to remain cautious on the battlefield.
However, Meade did not seem to think ahead towards pursuing Lee when the latter began to retreat towards Virginia. Had Meade begun preparing for such an eventuality after Pickett's Charge had been repulsed, the AoNV would have had a much more difficult time getting home. Any number of PODs could see the army trapped north of the Potomac and, quite possibly, forced to surrender.
If this happens, the war will surely end in 1864, if not late 1863. The South's best army would have been snuffed out of existence, with its best army commander and the cream of its officer corps now Union prisoners. While a scratch force (under Beauregard or Johnston) could have been put together in central Virginia to protect Richmond, it would have required stripping every other front of every soldier and even then probably couldn't have mustered more than 35,000 or 40,000 men.
There's still time for a fall campaign by the Army of the Potomac, which would be flush with victory. Richmond might well fall. With the need to reinforce Virginia, we might see Charleston and Atlanta fall before the end of 1863. I can see the war ending before Christmas.