You are talking about the guy who says "I am doing the best that I can." To Sonny Black right? That guy was based on Antonio "Bootsie" Tomasulo who would later be made after Sonny was killed. Pistone talks about how he had asthma real bad and sometime you had to give him a few minutes to talk and it would take a lot out of him. I think they added that voice box in the movie for effects.

"I have this Nightmare. I'm on 5th avenue watching the St. Patrick's Day parade and I have a coronary and nine thousand cops march happily over my body." Chief Sidney Green