Smells like a defective fuel pump - can supply adequate volume of fuel under normal driving but when gas pedal depressed carb injects a burst of fuel and engine has to wait for fuel flow to catch up - will splutter and lose power for a while until normal service is resumed. Take foot off gas and system fills up and regular power is restored until you pump the gas again...
Gentle acceleration = OK
Fierce acceleration = impossible
Peccavi
October 2008