Even if the Packers lose to the Patriots . . .
. . . as long as they beat the New York Giants AND the Chicago Bears . . .
. . . AND the New York Giants beat EITHER the Philadelphia Eagles OR the Washington Redskins . . .
. . . AND the Tampa Bay Buccaneers lose to EITHER the Detroit Lions OR the Seattle Seahawks OR the New Orleans Saints . . .
. . . then the Packers are in the playoffs.
That is an extremely likely scenario. Unless the Bears lose out, which I don't see happening, the Patriots game is irrelevant to the Packers' postseason prospects; neither beating nor losing to the Patriots affects their odds of making the playoffs in any way. In my opinion, given that they do not have to beat the Patriots to make the playoffs, they probably should not even try. The smartest course of action would be to bench Aaron Rodgers, Donald Driver, Clay Matthews III, and any other starters who are ailing. They should treat this game as another bye week and return the team healthy and rested for the final two games, which ARE must-wins. Doing this would give Matt Flynn some valuable snaps in a real gametime situation against a challenging opponent and improve the teams chances of beating the Giants and Bears.
Considering, however, that we have a coaching staff who was too bullheaded to let an opposing team score when it would have given the offense a fighting chance to stage a last-minute comeback, I don't see it happening.