ESPN had their division bloggers pick out a "can't lose" player, that without this player they probably don't have a chance of postseason play or Super Bowl aspirations. For the Bears, Kevin Seifert picked out Julius Peppers.
Chicago Bears: DE Julius Peppers. Peppers has been more responsible than any player for the rejuvenation of the Bears' defense since his arrival in 2010. Over that span, he has drawn top priority from opposing offenses but still managed to record 30.5 sacks and force seven fumbles. There is no substitute for a dominant pass-rusher. Perhaps most importantly, he has played through knee and other injuries to start all 48 regular-season games since the Bears signed him to a $64 million contract. It's no coincidence that defensive tackle Henry Melton has emerged to record 15.5 sacks over the same period. Without Peppers, the Bears wouldn't have a front-line player who can perform while drawing high attention from opponents.
Losing Peppers would be a huge blow, but I might actually put the Bears in the same boat if they lost Charles Tillman. There's one "proven" guy behind each that has to continue to show up (Corey Wootton for Peppers and Tim Jennings for Tillman), and a fair amount of "unproven/roster filler" (Kelvin Hayden a little more "proven" than Shea McClellin, say).
Offensively, you'd think about where the team would end up without Jay Cutler, but what about Brandon Marshall? The hope is that he doesn't have to do as much heavy lifting this year, but for as reliable a target as he was last year, and as big a part of the offense as he was last season, what happens to the offense if he gets hurt for the season? Do Alshon Jeffery and Martellus Bennett provide enough catches to power the pass game? The situation's much improved in the receiving corps, but losing Marshall would be a huge blow that could have some of the same impact.