The Patriots accomplished this once already in 2007. 16 wins vs. 12 wins for the rest of the division. None of the other years in the TB/BB era were particularly close. What makes it tough is "the field" automatically will get 6 wins because they have to play each other (unless there's a tie). I suppose a case could be made that could be canceled out by NE winning 6 games against their divisional foes. If that were the case, NE would need to get more wins in 10 remaining games than the rest of the division would in 30 games.
I don't think it is a slam dunk the Pats go 6-0 in the division (they don't play well @MIA). The Pats also have some tough non-divisional games (KCC, @NOS, HOU, CAR, @TBB, ATL, LAC, @DEN, OAK in Mexico, @PIT). Probably 5-1 in the division and 8-2 outside the division . . . so 13-14 wins. Call it 14. Not sure if the rest of the division is bad enough to go 8-22 outside the division.