It depends on the tribe. Now, when you're talking about some of the Southeastern tribes and the predecessor Moundbuilder cultures, they had something akin to professional armies and could amass at least a hundred warriors for battles with fairly short notice. They would have carried plenty of arrows plus there were probably apprentice warriors, younger men in training, who would have carried the reserve arrows. There was a Cherokee leader who once told a European he could amass a thousand warriors with a flick of his hand. That was probably no idle boast. Southeastern tribes had distinctions with bows, some being for hunting and others for war and, often, this was determined by poundage of the bow, war bows being of heavier poundage. It would make sense that there might be distinctions between arrows as well. If a people wanted to remain sovereign and had hostile neighbors, as nearly every tribe did have, then they would certainly have plenty of ammunition and go into battle prepared to win. Some tribes engaged in almost ritualistic warfare of raids and hit-and-run tactics while some tribes were in wars to garner more land or displace others from land they were sitting on that the wanted. But in any case, if you go into battle and you run out of ammo, you've got a problem. Because the enemy not only has ammo, but they could conceivably shoot yours back at you as well.
A civilization such as Cahokia could not have accomplished what they did without some sort of professional military. This has to go beyond each warrior doing what he feels doing. There would have had to be organization, to include arrowmaking on a much larger scale.
As far as how many arrows were carried, if there was some type of professional military, they would have had standardized equipment on some scale. Such as, going into battle, each warrior needs to have 40 arrows or something like this. More than likely, the answer to the question could be discovered by modern experiments. Find yourself a large quiver and start with 24 arrows, plus a stone-headed war club at your belt. Walk around with that all day and see how mobile you are. Then try adding more until it gets to the point your mobility is restricted. That number will be the maximum load you can carry into battle and remain mobile, able to move quickly to escape flanking manuevers and encirclement, or to exploit holes in the enemy formations. Modern armies do these experiments to determine optimum loads of ammunition soldiers can carry. (That's one reason the U.S. military went to the 5.56mm caliber round, to increase ammo load capabilities.) Nothing really changes under the Sun as far as logistics in warfare, so this experiment would provide a fairly accurate answer. There's no mystique as to the number of arrows since every ancient army had one goal in mind regardless if they're Native Americans, Celts, Romans, or Assyrians. That goal was to win the battles and, ergo, the war, with as few casualties as possible while inflicting the most casualties on the enemy. If you're relying on bowman, that costs arrows and you need to be willing to spend them.
