  We study an effective field theory of interacting nucleons at distances much
greater than the pion's Compton wavelength. In this regime the NN potential is
conjectured to be the sum of a delta function and its derivatives. The question
we address is whether this sum can be consistently truncated at a given order
in the derivative expansion, and systematically improved by going to higher
orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find
that the cutoff can be taken to infinity only if the effective range is
negative. A positive effective range---which occurs in nature---requires that
the cutoff be kept finite and below the scale of the physics which has been
integrated out, i.e. O(m_\pi). Comparison of cutoff schemes and dimensional
regularization reveals that the physical scattering amplitude is sensitive to
the choice of regulator. Moreover, we show that the presence of some regulator
scale, a feature absent in dimensional regularization, is essential if the
effective field theory of NN scattering is to be useful. We also show that one
can define a procedure where finite cutoff dependence in the scattering
amplitude is removed order by order in the effective potential. However, the
characteristic momentum in the problem is given by the cutoff, and not by the
external momentum. It follows that in the presence of a finite cutoff there is
no small parameter in the effective potential, and consequently no systematic
truncation of the derivative expansion can be made. We conclude that there is
no effective field theory of NN scattering with nucleons alone.
