The only way that deal would get done is if either team wants a player that badly, which is yet to be determined.
The Bears are a team that needs to win now. Head coach Dick Jauron doesn't have time to develop a quarterback as the team struggles. Another losing season could have him in the unemployment line a year from now.
The more unlikely scenario is the team trading up. The only player the Bears would consider trading up for is Carson Palmer. The USC quarterback is expected to go first, but the Cincinnati Bengals aren't sold on taking a quarterback with new defensive minded coach Marvin Lewis.
The team will still draft a quarterback, but most likely in round two. Jim Miller and a free agent quarterback more durable than Chris Chandler will compete for the starting role, which would allow a rookie to learn the offense and develop in a low-pressure environment.
If the team stays pat with the fourth pick the slot should produce an impact player, but at what position? The Bears have several needs with quarterback atop the list. However, if the team signs a free agent quarterback then drafting one isn't as high of a priority.