The problem with blitzing a team like the Pats is that it usually doesn't work. The Blitz can sometimes get to the QB, but even when it does, a good QB like Brady is just sitting there waiting for you to blitz, because it opens up the field for the pass. A couple plays that I recall before they cut away were completions on plays where either the Bears did a serious blitz, i.e. sending Bowman or the LB's, or plays where the LB's hung up on a play-fake. They both turned into solid, easy completions for Brady, because he got the ball out before the pressure could possibly get to him.
Maybe if they'd blitzed more, somehow they'd have turned things around, but I seriously doubt it. Brady is an MVP because he wants you to blitz him, and the times I specifically recall the Bears trying, Brady beat them.