There are a lot of people, especially in the YEC camp, that hold to the idea that death was impossible prior to the fall. They base this on the nature of the fall (esp Gen. 2:17; 3:19) and Paul's statement that death came into the world through Adam in Rom. 5:12. Those in the OEC camp don't have to believe this at all, because for many of them, the death that resulted from the Fall is spiritual death, that is, separation from God. Physical death existed prefall, especially in the animal kingdom.
I can't say for 100% sure which is right, but I think Vos makes a great point on it:
Geerhadus Vos wrote:. . . 'immortality' is used in the theological terminology for that state of man in which he has nothing in him which would cause death. It is quite possible that at the same time an abstract contingency of death may overhang man, i.e., the bare possibility may exist of death in some way, for some cause, invading him, but he has nothing of it within him. (Biblical Theology, 1975, p. 38)
As for me, I have not come to a firm conclusion, but it seems to me that either:
a) Man was created 'immortal' in the above sense, that is, death from an external cause was possible, but man did not have death "within himself"," or
b) Man was created completely mortal, in the sense that he would have died eventually even without sin, and the death that entered into the world was only spiritual in nature.
In either case, I think I would reject the impossibility of death, but then again . . . we could always be wrong ;)
God bless