I'm not going to fault him for this, as I too love The Godfather, both book and film, but I would like to clarify what he's talking about. This will involve a trip down memory lane, so be prepared.
When I took European Immigrant Literature in college, I was fulfilling a credit requirement for my English Education degree. Luckily, I loved the class, and never more than when we were reading The Godfather. What an assignment! I loved every second of it, and when we watched the movie (Part I), it blew me away. I know most people think of this as a "guy" film, but it's fantastic. Powerful, mesmerizing--the acting is insanely good. (You should, of course, know who's in the film--Brando, Pacino, Duvall.) I've seen it many more times since then, although I've never managed to force Mr. Cool to join me.
So I totally understand why Obama loves this movie. I respect him for making the choice to say he loves a gangster film over, say, Mr. Smith Goes to Washington, but his choice of singling out that first line rings false. Oh, sure, it's the first line of the movie, but it's said by Amerigo Bonasera, who has come to the Godfather for help. He has always believed in America, so when his daughter was brutally attacked by WASP boys, he trusted the American justice system to punish them. It failed him--they were released with just probation. Bonasera, though, wants more. He has always believed in America, but it has let him down. It has not given him the justice he desires--so he has come to ask the Godfather to kill the two young men. The Godfather refuses, and chastises Bonasera for not coming to him earlier. If he truly believes in America, he should accept the justice it provided. In the end, the Godfather does send some thugs to properly beat up the young men.
The idea throughout The Godfather is that while America is a land of prosperity, opportunity, and justice, if you are an Italian immigrant, you will be better served by the Family. There you can truly find prosperity, opportunity, and justice. Perhaps that is true for all of us--perhaps only in family can we find true fulfillment. Patriotism might only lead to disappointment.