I think 2 more wins puts us at like a 40% chance of making the playoffs (not based on any math, just my own guesstimate). The issue is, you have the following teams that can play under .500 the rest of the year and still finish 10-7: Lions/Packers (whichever doesn't win the division in a scenario where the Bears finish 10-7), and 2 of the Rams/Seahawks/49ers.
If the Bears finish 2-4, at least 3 of those losses will come against the NFC and at least 1 of them would come against the Lions or Packers. They play SF H2H, so if the 2-4 comes with a loss to them, SF wins the tiebreaker. If the Packers win the division, one of the Bears wins would need to come against the Lions to have a shot at the tiebreaker over them (both teams are 1-2 against the North). If the Lions win the division, the Bears would need to sweep the Packers or go 1-1 and hope the Packers lose 2 more division games since they are 2-0 in the division.
All that to say, the Bears should aim for at least 3-3 to feel good about the playoffs.