It means that he is happy that The Avengers film is a good film which people like. In the past, he has had to press interviews about films which aren't very good and which the public don't like. Even so, the actors are always expected to carry on with their normal press interviews, being positive about the film.
So "walking the press line" means "undertaking an actor's obligations to do interviews with the press/media" and a "turkey" (in this context) is a film which has not been successful.
Student or Learner