First "carrying capacity" is a fairly vague term. In theory, the term means the absolute maximum number of deer that could inhabitat an area until lack of food causes density to stop increasing due to high malnutrition-related mortality. In essence, the point when the herd would stop growing (annual recruitment of new deer through reproduction equals annual mortality).
However, most don't use the term like that. They refer to carrying capacity as the density at which deer can exist at fairly healthy levels. But even that is a problem, as there is no destinct "cut-off point" for "fairly healthy." Deer herds are density dependent, in that as density increases, herd health declines. What is the definition of fairly or relatively healthy? As density slides up the scale, health/productivity/growth-potential slides down the scale.
But to answer your question, carrying capacity--where ever you want to place that limit--is highly variable. A deer requires approximately 2,000 to 2,500 pounds of dry-weight (water removed) food per year. Each different habitat will produce a different amount of deer food per acre per year. An agricultural field may produce 10,000+ pounds of deer food per acre per year. At the opposite end of the scale, a mature hardwood forest may only grow 10 pounds of deer food per acre per year (minus acorn production).
Using some VERY over-simplistic calculations, a square mile (640 acres) of agricultural could feed virtually an unlimited number of deer, yet a square mile of mature harwood forest in a poor acorn year may only support 3 or 4 deer.
So yes, carrying capacity varies DRAMATICALLY by habitat type, and that is why habitat management is such a powerful tool in small-land management.