Classic/Antique Car Repair: fuel problem on 72 vette, edelbrock performer intake, good luck jack

Question
i have a 1972 corvette with a 350(original motor) modified with an edelbrock performer intake and carb, also switched to elec ignition. it has a glass inline fuel filter, when i start the car the filter fills up with gas as it should, but as it runs the fuel level in the filter decreases(at idle) slowly down to no fuel and cuts off. now it is very hard to start. when it does start , it wont run at idle. i first noticed this while driving for long periods, the car would cut off at stop lights and when i would accelerate hard the engine would sputter and backfire through the exhaust. the car runs fine when first started but gets worse over time. could this be a sign of a failing fuel pump or something else?

Answer
Sounds like the engine is starving for gas.  Check the fuel pump and make sure the fuel line from the tank is not blocked. The pump may be good and sucking a buble in the gas line.  Blow backwards through the line to the tank and see what happens.  It should be clear.  
I really know about Model a's, but I hope this helps.
 Good luck.
jack