I was driving a car with an overly full gas tank. After about 20min of driving, I pulled into a parking lot and the engine died. After waiting about 15min with the hood open (I thought it might be a heat issue as it was hot out), the car started fine.
As @Moab stated, overfilling the gas tank will not cause an issue with the fuel pump. In fact, the fuel pump likes there to be fuel in the tank. If there's not enough fuel, you can overheat the fuel pump ... but no way to cause it issues with too much gas.