Recent studies indicate that growing streamwise perturbations driven by streamwise vortices and the resulting Reynolds stresses play a significant role in both the transition to turbulence and the near-wall turbulent flow. In this note, we show that viscoelasticity introduces a negative feedback, so that the streamwise flow driven by a streamwise vortex would have the effect of diminishing the vortex. The terms responsible for this effect are the same as these that lead to a second normal stress difference.