One little hint of things to come:
In a deleted scene from II, Neri (in the boathouse at Anthony's party) shows Michael a photo of Fabrizzio and says, "He entered this country in 1956, sponsored by the Barzini Family"[emphasis added]. It suggests that, even a year after the Great Massacre, some anti-Corleone people in what remained of Barzini's family were still active, or at least saw the need to pay off Fab for betraying Michael when he was in Sicily.