Need help with stumbling engine

[newschool]

I have a 350 with a 1406 carb. It often sits several days without being started. When I first got the truck it ran fine. I then replaced the rotted cab and fuel tank. Now things are a mess. It only runs correctly now when its between medium and heavy acceleration. Other wise it stumbles and has no power. It has never backfired through the carb or exhaust. What has me baffled is I drove it last week (30miles) to pickup some hay and it ran just fine. I drove it yesterday and its back to running like crap. I rebuilt the carb this morning and put it back on the truck and there is no difference. It looks like it has a newer fuel pump on it. I changed the fuel filter after I changed the fuel tank and then about 2 weeks after that. The fact that it ran great for one day is a mystery. Any sugestions on what could be the problem.