The Saints can only get in via the division at eight wins. Two divisions (NFC East, NFC North x2) have their reps clinched already. That leaves two divisions (NFC South, NFC West) still up for grabs, and two wild-card spots. Washington already has nine wins so the Saints can’t pass them. The Rams currently hold the division and have the +1 on the Saints, which means it’d be more beneficial to the Saints for the Rams to keep winning… except Green Bay has ten wins and a match vs. the Saints tomorrow.
As for the division: technically the Falcons can still lose 10 games. Technically the Bucs can still be caught at 8-9 on division record; losing out would put them at 2-4 in division games, whereas the Saints would land at 3-3. None of these scenarios is likely to break the Saints’ way. Time to play spoiler