An experimental investigation of the effect of fluid rheology on air entrainment in plunging tape experiments (dip coating) was carried out. The critical velocity at which the dynamic wetting line breaks up, allowing air to entrain into the liquid, was measured for a range of viscoelastic polymer solutions in glycerin/water mixtures. Variations of the critical velocities with various solutions were found to be unexpectedly small in comparison with the large viscosity variations. The results suggest that dynamic wetting failure and subsequent air entrainment are governed by nonhydrodynamic phenomena occurring at the molecular scale at the wetting line. It was also found that fluid elasticity gives rise to flow instabilities that may lead to a different, hydrodynamic mechanism of air entrainment.