  Low energy theorems are derived for the coefficients of the effective range
expansion in s-wave nucleon-nucleon scattering valid to leading order in an
expansion in which both $m_\pi$ and $1/a$ (where $a$ is the scattering length)
are treated as small mass scales. Comparisons with phase shift data, however,
reveal a pattern of gross violations of the theorems for all coefficients in
both the $^1S_0$ and $^3S_1$ channels. Analogous theorems are developed for the
energy dependence $\epsilon$ parameter which describes $^3S_1 - ^3D_1$ mixing.
These theorems are also violated. These failures strongly suggest that the
physical value of $m_\pi$ is too large for the chiral expansion to be valid in
this context. Comparisons of $m_\pi$ with phenomenological scales known to
arise in the two-nucleon problem support this conjecture.
