Help with my toilet pump?

My toilet lately has been flushing but not refilling the tank with water. When I flush the toilet, it sometimes will refill. Mostly, the water just RUSHES out so quickly, the pump never kicks in. I recently discovered that if I "bounce" or jiggle the pump, it will trigger the tank to refill. Is there something I can do (short of replacing the pump) so that it refills after every flush?