The authors designed four experiments to test the hypothesis that performance is particularly undermined by time pressure when people are avoidance motivated. They reported that their results suggest that given its nature and implications, it seems best that avoidance motivation is avoided in situations that involve (time) pressure.
Roskes, Marieke, Elliot, Andrew J., Nijstad, Bernard A., and De Dreu, Carsten K.W. (2013). Time Pressure Undermines Performance More Under Avoidance Than Approach Motivation. Personality and Social Psychology, 39, 803-813.