I doubt if the fuel pump would do that, you would probably have stumbling or sort of a engine miss if the fuel pump was not delivering enough fuel.
You can check the fuel pump with a pressure gauge, should read over 4lb or real close. another test would be to do a flow test this can be done by starting the engine to make sure the carburetor is full then shut the engine off disconnect the fuel line put a hose on the end of the line or have a friend with container that they can place to catch the fuel, start the engine and let it run long enough to check the flow or till you run the gas out of the carburetor just make sure that you won't splash any fuel as it comes out, you should have steady flow.
I don't think that its the fuel pump though, sounds like it could be plugged main jets in the carburetor or the distributor is out of time due to point adjustment and or no vacuum advance.
You didn't say if this happened suddenly or over a period of time, this could be your engine is getting tired and in need of a overhaul.