  We use Monte Carlo simulation to probe the phase structure of a SU(2) gauge
theory containing $N_f$ Dirac fermion flavors transforming in the fundamental
representation of the group and interacting through an additional four fermion
term. Pairs of physical flavors are implemented using the two tastes present in
a reduced staggered fermion formulation of the theory. The resultant lattice
theory is invariant under a set of shift symmetries which correspond to a
discrete subgroup of the continuum chiral-flavor symmetry. The pseudoreal
character of the representation guarantees that the theory has no sign problem.
For the case of $N_f=4$ we observe a crossover in the behavior of the chiral
condensate for strong four fermi coupling associated with the generation of a
dynamical mass for the fermions. At weak gauge coupling this crossover is
consistent with the usual continuous phase transition seen in the pure
(ungauged) NJL model. However, if the gauge coupling is strong enough to cause
confinement we observe a much more rapid crossover in the chiral condensate
consistent with a first order phase transition
