We prove a query complexity lower bound for $QMA$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $SBP^A \not\subset QMA^A$, resolving an open problem of Aaronson [2]. Our proof uses the polynomial method to derive a lower bound for the $SBQP$ query complexity of the $AND$ of two approximate counting instances. We use Laurent polynomials as a tool in our proof, showing that the "Laurent polynomial method" can be useful even for problems involving ordinary polynomials.