Looking at the Simulations that are out there thins look not so good.
A) Football Outsiders:
FO Playoff Odds
They value "the lots of short stuff" offense rather high and believe and bend but dont break, so they have the Pats as one of the top teams in the league.
Therefore Pats are mostly sure to win their division, but even in that case its 50/50 if the get a bye or not, because HOU and DEN have such easy schedules.
Given the very favorable estimation of the Pats real strength, and the fact that I cannot find any overrated AFC Team in there estimations, I would guess this is the best case scenario.
B) Advanced NFL Stats
Adv. NFL Playoff Odds
They value our Big Play defense very poor and also see the Offense as merely good as opposed to breathtaking which adds up to a perfectly average team. Given the tenhdency of the AFC to field losers this year it still gives us the best shot at a divisoion title (68%) but even when we get there we have only 15% chance of getting a bye.
Again, I don't think we can be much worth than that one, so 15% is kind of worst case.
So we are still in the race, but it will be a uphill battle to get there and we should expect to win 4 Playoff games this year, which at least means 30% more endorphines.
PS: For all people unaware of the method behind this projection, in both cases the team strength estimation is calculated in a winning probability for each game. and then the season is simulated 10000 times based on these probabilities.