running poorly

1974 454cid stock everything save for Accel HEI
I can't seem to get this thing to consistantly run well. I have the carb set but everytime I let it sit for a day or two then start it up, it sounds very rough (Kinda like it is missing on the right bank). I run it hard for awhile(hour?) and it starts to run smooth. plugs fouling? It is NOT running rich, lean if anything.
My mechanic(I am a newbie) tells me that it is the carb and it needs a rebuild. He also says I need a new fuel pump. I am not convinced.
Suggestions?

If it was the carb or fuel pump it wouldn't clean up after it ran for awhile. I would be suspicious of the Accell dizzy. Do you have a stock one to check with?

454 has high miles. I get a sticking lifter every so often, less now that I have run some Cfoam through. Accel unit(and car) did sit for quite awhile.(few years) I think this is part of the issue as well. I will open it up and check for cracks or corrosion. I also have to feather the gas pedal in order to get it to wind up even after running smoothly.

Check your vacuum lines and take a look at your wiring. The vacuum lines may have gotten hard and cracked, and anything that has been sitting for a couple of years may have had mice, rats or some type of critter that like to chew on your wires. (happened to me)