If Dallas and Chicago tie at 10-6, it will be almost impossible for the Chicago to win a tiebreaker. If the tenth Dallas win is against Philadelphia, then Dallas wins the tiebreaker on conference record.
If the tenth Dallas win is against Baltimore, then Chicago would have to win the strength of victory (the combined record of the opponents in all of a team's wins). Currently, Dallas has a strength of victory of 54-70-2, and Chicago has a stength of victory of 41-70-1. Assuming that Dallas beats Baltimore and loses to Philadelphia and that Chicago beats Green Bay and Houston then their respective strength of victory would be 63-77-2 (Dallas) and 53-88-1 (Chicago). In this case, Chicago would need the following results to happen in order to win the strength of victory:
Week 16
St. Louis over San Francisco
San Diego over Tampa Bay
Detroit over New Orleans
New York Jets over Seattle
Houston over Oakland
Minnesota over Atlanta
Philadelphia over Washington
Carolina over New York Giants
Week 17
St. Louis over Atlanta
Jacksonville over Baltimore
Kansas City over Cincinnati
Detroit over Green Bay
Indianapolis over Tennessee
Minnesota over New York Giants
New Orleans over Carolina
Pittsburgh over Cleveland
Oakland over Tampa Bay
Arizona over Seattle
If all of that happened, then Chicago (68-91-1 SOV) would earn the 6th wildcard over Dallas (67-91-2 SOV) and Philadelphia (10-5-1) would be the 5th wildcard. If even ONE of those games is decided opposite to how it is listed, then Chicago would lose out to Dallas in a tiebreaker.
So basically, if Dallas beats Baltimore Saturday night, Chicago, for all intents and purposes, cannot catch Dallas.