All of the wild card tiebreakers pretty much go to all the other teams ahead of the Saints, so the only realistic path to the playoffs was to win the division, and that pretty much faded away when the Saints lost to the Rams and the Bucs won.
Now, it doesn't matter if the Saints beat Tampa or not, because even if the Saints win the Panthers (lol) would have to beat the Bucs in the last game of the season and the Saints would still have to beat the Falcons.