That is the classic symptom of the main jet area of the carburetor being clogged or dirty. You don't state your model number so your carb may be different from the picture but you need to clean the main nozzle and main jet areas of the carburetor. Typically you would remove the carb from the engine to do this and clean all the passages with carb cleaner....paying close attention to the path that the fuel takes from the bowl up into the throat.
The fuel pump can easily be checked for correct function by noting if your primer bulb looses firmness when the engine is running, or dis-connecting the hose from the pump to the carb and check for fuel flow when the engine is running.
However, needing the choke to run is not a fuel-pump related symptom.