If you can blow through the fuel inlet, the pump should be able to provide plenty of gas to the carb. Have you determined that the pump is actually pumping gas yet? You can loosen the two bolts that attach the pump to the engine a couple of turns each, and work the pump housing up and down by hand to see if you can get it to move a little more gas. Once the pump and the fuel lines are full, it should supply enough gas to the carb to keep the engine running.
Jerry
