Many commonly-used auction mechanisms are ``maximal-in-range''. We show that any maximal-in-range mechanism for n bidders and m items cannot both approximate the social welfare with a ratio better than min(nm) for any constant 12 and run in polynomial time, unless NPPpoly . This significantly improves upon a previous bound on the achievable social welfare of polynomial time maximal-in-range mechanisms of 2n(n+1) for constant n. Our bound is tight, as a min(n2m12) approximation of the social welfare is achievable.