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 $\min(n, m^\eta)$ for any constant $\eta < 1/2$ and run in polynomial time, unless $NP \subseteq P/poly$. 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 $\min(n,2m^{1/2})$ approximation of the social welfare is achievable.