The J2 should have a L type, low pressure pump mounted in the engine compartment. About the only thing that will cause the rapid running you describe would be an air leak between the tank and the pump as Dr E. suggests. The other thing would be no fuel in the tank (the ultimate air leak). If I remember correctly, the J series didn't have any fuel gauge or low fuel light, instead having two lines running from the tank to a two way valve that controls which line supplies fuel to the carburetors. One position of the valve selects the line attached to a stand pipe in the tank (normal position). Upon running out of fuel from the stand pipe, the valve is switched over to the auxiliary line that draws fuel from the bottom of the tank - this supplies another couple of gallons of fuel to get you to a filling station. Of course this arrangement has one major drawback - if you don't switch the valve back to the primary position, the next time you run out of fuel, the tank is actually empty because you were drawing fuel from the very bottom of the tank.
Cheers,