No, he's actually quite sane. (We won't judge his dating choices.) It's not at all crazy to think that the Bears can win the Super Bowl.
The parity in the NFL is reaching frightening levels. No team is undefeated, but that's only the tip of the iceberg.
Think about what's happened to the teams the Bears have played. The Bears lost to the Giants and Redskins, but beat the Eagles and Vikings. The Eagles beat the Giants and the Vikings beat the Redskins. There is not one dominant team who has an easy walk to Super Bowl XLV.
Why not the Bears? They made it to the Super Bowl in 2006, led by a dominant defense, explosive special teams and a competent offense. If play against the Patriots and Jets like they did against the Eagles, there is no reason to believe that they can't turn it up in the playoffs.
Grizzly Detail is with you, Cutler. Bears to the Super Bowl -- get on board!