Last season, the Green Bay Packers pass offense struggled against the Bears defense. They were held to under 20 points in six regular season games, and the Bears did it to them twice. Looking at Aaron Rodgers's game-by-game stats, he cruised through the post-season except he hit a giant pothole against the Bears in the NFC Championship game. He wasn't too impressive against them in 2009 either when he threw for only 1 TD pass in 2 regular season games.
However the Bears are currently hurting in their secondary with injuries at safety. If Chris Harris plays, he has a decent chance to start, they should be fine. I asked Kev H at Windy City Gridiron about those injuries:
Q: Depth appears to be a problem at safety with injuries to Chris Harris and Major Wright. Who do you expect to play out there on Sunday? Any concerns with the backups?
A: Harris is in limited practice right now, and as of this writing, (late Thursday night) I'd be too hesitant to count him out just yet for Sunday. Wright is definitely going to be out this weekend. If Harris can go, you're going to see Brandon Meriweather and Harris. If Harris also can't go, you're likely to see Meriweather and Craig Steltz, or possibly Chris Conte.
It's not a huge position of depth for the Bears, unfortunately, as they're not particularly deep at any position. Not having Harris is a big one, as he brings a lot of veteran presence back there. We haven't seen too much Meriweather in action yet, but he's working himself in, and will probably be taking that job from Major Wright before too long. (They didn't pay him starter money to be a backup.) Wright's had a lot of issues with the angles he's taken lately, and poor tackling and coverage in general. He probably needs another year to really be at the level most of us would like to see, but the decision to let D. Manning go in the offseason showed us the Bears are committed to a new future in the defensive backfield.