At Antietam, McClellan certainly didn't have a large reserve, by 4pm every single division was either in the line or shattered. The extreme attritional fighting on the Union right meant that between 1st, 2nd and 12th Corps had a single intact division between them, and had to be extracted from contact by committing 6th Corps (which McClellan wanted to commit to the left, but pleas from Meade that he was about to be overrun changed his mind. Actually a major opportunity for Lee to destroy the AoP was squandered on that flank when Stuart gained the Union flank, but didn't actually attack).
There was an awful lot of Union artillery up there, and the Confederate left had been slashed and gashed just as badly as the Union right. There wasn't much strength up there.
As to Stuart attacking, here's what he says in his report:
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This fire was kept up with terrible effect upon the enemy, and the position of the artillery being somewhat endangered, Early's brigade was sent to me by General Jackson as additional support. The enemy had advanced too far into the woods near the Dunkard church for the fire to be continued without danger of harming our own men. I accordingly withdrew the batteries to a position ****her to the rear, where our own line could be seen, and ordered General Early to rejoin his division, with the exception of the Thirteenth Virginia Infantry, commanded by Captain [F. V.] Winston, which was retained as a support for the artillery. The artillery opened from its new position, at close range, upon the enemy with still more terrible effect than before. The Thirteenth Virginia Infantry, being within musket range, did telling execution. Early's division now pouring a deadly fire into their front, while the artillery and its support were bearing so heavily upon their flank, the enemy soon broke in confusion, and were pursued for half a mile along the Williamsport turnpike. I recognized in this pursuit part of Barksdale's and part of Semmes' brigades; and I also got hold of one regiment of Ransom's brigade, which I posted in an advantageous position on the extreme left flank
after the pursuit had been checked by the enemy's reserve artillery coming into action. Having informed General Jackson of what had transpired, I was directed by him to hold this advance position, and that he would send all the infantry he could get in order to follow up the success. I executed this order, keeping the cavalry well out to the left, and awaiting the arrival of re-enforcements. These re-enforcements were, however, diverted to another part of the field, and no further engagement took place on this part of the field beyond a desultory artillery fire
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Jackson's report says:
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In the mean time General Stuart moved his artillery to a position nearer to the main command, and more in our rear. Early, being now directed, in consequence of the disability of General Lawton, to take command of Ewell's division, returned with his brigade (with the exception of the Thirteenth Virginia Regiment, which remained with General Stuart) to the piece of wood where he had left the other brigades of his division when he was separated from them. Here he found that the enemy had advanced his infantry near the wood in which was the Dunkard church, and had planted a battery across the turnpike near the edge of the wood and an open field, and that the brigades of Lawton, Hays, and Trimble had fallen back some distance to the rear. Finding here Colonels Grigsby and Stafford, with a portion of Jackson's division, which formed on his left, he determined to maintain his position there if re-enforcements could be sent to his support, of which he was promptly assured. Colonel Grigsby, with his small command, kept in check the advance of the enemy on the left flank, while General Early attacked with great vigor and gallantry the column on his right and front. The force in front was giving way under this attack when another heavy column of Federal troops were seen moving across the plateau on his left flank. By this time the expected re-enforcements (consisting of Semmes' and Anderson's brigades and a part of Barksdale's, of McLaws' division) arrived, and the whole, including Grigsby's command, now united, charged upon the enemy, checking his advance, then driving him back with great slaughter entirely from and beyond the wood, and gaining possession of our original position. No further advance, beyond demonstrations, was made by the enemy on the left.
In the afternoon, in obedience to instructions from the commanding general,
I moved to the left with a view of turning the Federal right, but I found his numerous artillery so judiciously established in their front and extending so near to the Potomac, which here makes a remarkable bend, as will be seen by reference to the map herewith annexed,
as to render it inexpedient to hazard the attempt.
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While there may have been an opportunity there, Stuart didn't have the strength to do anything about it, and the constant meatgrinder to the south ate up any reinforcements he might have been sent. Even if you reverse that, it doesn't sound like the attack could have been anything but desperate, with very heavy casualties if it succeeded or failed. That would have left Jackson unable to do much after breeching the line -- and McClellan would still have had reserves available.
Tim