An old gunslinger by the name of Brett Favre. Now, with the Dome Patrol in full force, featuring defensive player of the year Pat Swilling, a rookie Brett Favre and Marcus Allen, the Saints look primed for a run in a year the NFC was slightly down.
A run they do enjoy. Even with Favre a bit erratic, the defense and Allen's running is still enough for the Saints to get in the playoffs. There, they are able to actually defeat the Atlanta Falcons in the wild card, and travel to the Motor City to take on the Detroit Lions. There, the defense is able to keep Barry Sanders at bay, and the Saints have a date to Washington, who are fresh off of a win against their hated-rival Dallas Cowboys. Unfortunately, that's where the journey ends, as Washington's 1991 team is one of the more slept-on great teams in NFL history.
By 1992, with Favre coming into his own as a leader a year early, and four Pro Bowl linebackers, the Saints get past the Eagles in the Wild Card round in this world, and go on to face the future champion Cowboys, who get the better of the Saints.
Unfortunately, even with Favre, the combination of an aging Marcus Allen and linebackers, coupled with the juggernaut San Francisco 49ers (in their division) and Cowboys, the rest of the 1990s goes about the same, except with the Steve Young-led 49ers in a couple more Super Bowls.
As for the 2000s though...