Dying problem

I just got my 64 Dart GT a couple months ago and it has a 225 slant 6. About a week after i got it something broke in the engine destroying the crank shaft. I had the whole engine rebuilt and it runs ok but with a little problem. It is slow to start up in the morning, i have to keep turning it over and about 3 min later it will fire up. After i get started if i hit the gas just a little too much it starts to flutter and die unless i let off the gas. After it warms up it doesnt do it as bad if at all. The shop that rebuilt the engine told me i might need the carb rebuilt or get a new one. Could that be the cause of both of those problems?