1
general::
A goal that is hard to fulfill or achieve, as in Getting a thousand new subscribers is a tall order indeed. This expression uses tall in the sense of "impressively great" or "difficult." [c. 1900]
American Heritage Idioms
2
general::
Phrase(s): *a tall order
a request that is difficult to fulfill. (*Typically: be ~; give someone ~.) • That’s a tall order. Do you think anyone can do it? • Well, it’s a tall order, but I’ll do it.
McGrawhill's American Idioms And Phrasal Verbs