score:2
Confederate resupply capability at Gettysburg was virtually nil. The North even had units near Frederick and Harper's Ferry on the line of communication. These were no match for the army, but could interdict a wagon train.
So a indefinite stalemate at Gettysburg would have required a Confederate retreat. At the end of the battle, there was still ample food, and small arms (rifle) ammunition for more fighting. Artillery solid shot was virtually out in the 1st and 3rd Corps batteries that bombarded the Union position, so they could not have repeated that. They had ample canister which would come into play if the Union attacked their position in turn.
With the army concentrated, foraging for food was limited, and the ammo would not last forever, but there was some left, especially for defense. But Lee would have to retire towards the Potomac absent a crushing victory for resupply sooner rather than later.
Upvote:5
The battle grew from an initial reconnaissance by Hill's corps to determine if the shoe factory in Gettysburg had sufficient quantities to resupply several Confederate units with boots (or shoes).
I think that completely summarizes the Confederate supply situation for most of the war: not just pillaging for food, but pillaging for footwear (arguably second only to his rifle in importance for an infantryman, and challenged only by his spade) because the Confederacy was unable to supply any.
The notion that both sides used the bayonet during Picket's charge because they were low on ammunition borders on absurdity; they used the bayonet because they were in close physical contact, and a bayonet is much faster in close quarters than reloading to fire a bullet. No-one stops to reload in a bayonet fight and lives to tell the tale.
Update: I do not mean to imply in that last paragraph that the units on Cemetery Ridge, of both sides, had ample ammunition. The troops on the ridge were undoubtedly low, having fired most of what each carried in a cartridge box while closing to contact. And after nearly three days of battle, both armies had to be running short on ammunition at hand, the Confederates likely worse off then Meade. That fact is irrelevant to the tactical situation on Cemetery Ridge; having closed to contact, both sides were forced into a bayonet duel.
The point of closing to contact is to defeat the opponent with the bayonet.
Both commanders likely expected that if successful in closing to contact, the Confederates would win out unless very badly outnumbered; due to their greater morale, their greater experience on average, and their greater desperation. Unfortunately for Lee, the casualties incurred in mounting Cemetery Ridge, combined with Stuart's inability to swing around the Union right and Meade's prescience the evening before, resulted in just such an outnumbering.