My apologies, I interpreted "running out of space" as meaning running out of memory, rather than meaning overflowing the stack.

The tail recursion part isn't right though. If it isn't optimised into a loop, then tail recursion makes no difference at all, you will overflow the stack just as rapidly, not later. If it is optimised into a loop, then you will not overflow the stack at all.

Someone who doesn't believe that stack is "space" will not believe that it's "memory" either. :)

I think "space" (i.e. in "run out of space before you can terminate") is most naturally interpreted as referring to memory.