We have created a quantum degenerate Bose-Fermi mixture of
23Na and
40K with widely tunable interactions via broad interspecies Feshbach resonances. Over 30 Feshbach resonances between
23Na and
40K were identified, including
p-wave multiplet resonances. The large and negative triplet background scattering length between
23Na and
40K causes a sharp enhancement of the fermion density in the presence of a Bose condensate. As explained via the asymptotic bound-state model, this strong background scattering leads to wide Feshbach resonances observed at low magnetic fields. Our work opens up the prospect to create chemically stable, fermionic ground-state molecules of
23Na-
40K, where strong, long-range dipolar interactions would set the dominant energy scale.