Jeremy: Are you still running the old Carter W/O carb? If so, there may be something wrong in the high speed circuit. The metering rod could be screwed up or the metering rod jet could be gummed up. There could also be something clogging the tip of the main nozzle. The low speed (idle) circuit operates differently which may explain why it craps out when you touch the throttle. When it's idling, the fuel / air mix enters farther down in the carb throat by the throttle valve, and also through the idle adjusting screw seat. Again, since you are running at idle, it makes me think that there's something wrong in the high speed circuit... mayb some laquer from old gas sitting in the bowl or something.
On the more PITA side (ask me how I know
) the offset lobe on the cam shaft that operates the fuel pump lever may be badly worn. In this case, it's just not going to pump up enough fuel when you move the throttle past idle speed.
I can probably track down one of my old Carter spec sheets if you need it. Shoot me an e-mail and let me know what model carb you have. I bought the Willys section of a carter carb service manual off of E-bay.