  We discuss the emergence of an orthogonality catastrophe in the response of a
composite fermion liquid as the filling factor \nu approaches 1/2m, where
m=1,2,3.... A tunneling experiment is proposed in which dramatic changes in the
I-V characteristic should be observable as \nu is varied. Explicit I-V
characteristics calculated within the so-called Modified Random Phase
Approximation, are provided for \nu=1/3 -> \nu=1/2.
