Let's run through 'em.
- Division: The Saints need to win out, the Bucs need to lose out. That would leave the Saints at 9-7 and the Bucs at 8-8. Any ties automatically go to Tampa because of head-to-head record, the first tie-breaker. They also play Atlanta, San Francisco and Carolina. So ... yikes.
- Wild Card Scenario 1: Here's your less likely more likely scenario. There are two potential wild card teams in front of the Saints. The Giants are 9-4; the Saints would have to win out while the Giants lost out (Washington, Buffalo and New England). Both teams would be 9-7, but the Saints (8-4) would have a better conference record than the Giants (7-5). Hence, they would win on the second tie-breaker. This matchup can't go to common opponents.
- Wild Card Scenario 2: This is your most likely scenario. The Vikings are 7-6, meaning that the worst they can do is 7-9. If the Saints tie that mark it would go to conference record. The Vikings are currently 5-5, meaning that they could finish anywhere between 5-7 and 7-5. The Saints are 5-4, and could finish anywhere between 8-4 and 5-7 in conference. They would need to tie the Vikings in wins and beat them in conference record to win that tie-breaker. The third tie breaker is record against common opponents, with a minimum four games. If my understanding of the rule is correct, the common opponents are Atlanta, Chicago, Philadelphia and San Francisco (5 games each). With Chicago still to play, the Vikings are 3-1 against common opponents. With Philadelphia and Chicago still to play, the Saints are 3-0.
Any way you slice it, the Saints need to win out and get a lot of help.