Fuel delivery problem; maybe?

The 70 Dart slant 6 with the holley 1920 carb is have an odd problem. It will start right up and die. I can keep it running if I keep the starter engaged but as soon as I release the key the engine shuts down. I ordered the carb rebuild kit and did the rebuild tonight but it is still doing the same thing. The fuel filter has a air bubble that does not go away even while I keep the starter engaged. I did pull the fuel line and the pump is pumping; I did not test the pressure. This is what I believe may be wrong:
1) I rebuilt the carb incorrectly
2) The fuel pump is bad just not pumping the correct pressure

Thank you as always for any help or ideas