Not with Brees. Typically teams focus on "running the ball" as a key to success because the passing game tends to be inconsistent. I mean 40% of most pass plays end in incompletions stopping the clock, then you throw in sack potential (which are drive killers) and interceptions (which are drive killers and field position killers), running seems a lot safer (it is).
So a team that runs well never seems to lose games it leads in because it never screws up and always shorterns the game (Pittsburgh).
BUT
There are exceptions. Notably is the Charlie Weis coordinated Patriots who were heavily pass first, second, run a draw play, then pass it three more times. The reason that worked was the faith they had in Brady.
I think we've got a similiar situation here. Brees was, what, 8-8 on that killer 8:30 drive vs Philly? Brees is like a well oiled running game. He just doesn't screw up. He doesn't take sacks, he rarely throws picks, and when he needs too, he always seems to complete the pass. That's as good as any running game, right?