In this situation I recommend you pull the carburetor off and remove the fuel bowl, then the float. Inspect the tip of the needle for damage. There is also a chance that some debris got into the fuel inlet and got stuck in the seat. Make sure the float is not full of fuel, if it is, it needs to be replaced.
This is likely a (passive) electric diaphragm type pump, and the internal diaphragm is coming apart. This pump normally functions all the time with key on power. The float and needle are what controls the flow inside the carburetor.