I believe it's 100% not possible that the Jets could make the playoffs and play the Patriots during the 1st round.
I love threads like this, I do know that it's possible for the Jets and Patriots to play one more time this season; it would then be during the AFC Championship game which would be something amazing to watch happen.
The Jets would become the 5th seed of the AFC Playoffs with a W this week against the Bengals. The Ravens would then become the 6th seed with a W this week.
The Jets would have to beat the Bengals and the Patriots would have to beat the Ravens during the WC games.
The Jets would have to beat the Colts on the road, while the Patriots would have to take out the Chargers out in SD.
The Jets would then be playing the Patriots, in NE, on the road, for a chance to play for a trip to the SB during the AFC Championship game.