  Recent studies suggest that coalescing neutron stars are subject to a fluid
instability involving the nonlinear coupling of the tide to $p$-modes and
$g$-modes. Its influence on the inspiral dynamics and thus the gravitational
wave signal is, however, uncertain because we do not know precisely how the
instability saturates. Here we construct a simple, physically motivated model
of the saturation that allows us to explore the instability's impact as a
function of the model parameters. We find that for plausible assumptions about
the saturation, current gravitational wave detectors might miss $> 70\%$ of
events if only point particle waveforms are used. Parameters such as the chirp
mass, component masses, and luminosity distance might also be significantly
biased. On the other hand, we find that relatively simple modifications to the
point particle waveform can alleviate these problems and enhance the science
that emerges from the detection of binary neutron stars.
