The simple answer to this question is no. However, size does matter in this situation. If you have small breasts, you will need to nurse a little more frequently to maintain your milk supply at the same level as those who have larger breasts. The science behind this principle goes something like this:
As your breasts become fuller, the tightness or engorgement of the breast tissue signals the milk producing glands to slow their milk production. Women who have larger breasts can hold more milk before their breasts begin to get engorged with too much milk. Keep in mind, however, that milk production is not solely governed by breast fullness or emptiness.
A bigger factor determining how much milk will be made is the stimulation that the breast receives from a nursing baby. During nursing, the breast is stimulated to produce more milk than when it otherwise would between feedings. Nursing is even more effective than using a breast pump. The key is emptying the breast as much as possible. However, you can't empty it all the way, just like you can't empty a river.
The more frequently the breasts are emptied, the more rapidly they will fill, and the more milk you will make in a 24 hour period. When a baby goes through a growing spurt she will nurse more frequently and often be cranky about how much milk she is getting, if she is not getting enough. As your milk supply catches up with your baby's demand she will begin to nurse less often again, getting more milk at each feeding.
So as you can see, having big breasts does not determine how much milk you make on its own, but it may influence how often you need to nurse to maintain a certain amount of supply.
