Now remember these are more based on what if scenarios, so don't take it too seriously, but consider the following:
Niles Paul hits the ground running (and opposing defenders on running plays) and looks to be a very capable TE. He immediately becomes the Redskins best blocking TE (not that it is tough to do), and shows himself to be a weapon in the preseason and practice. Chris Cooley comes back fully healthy and looks poised for a big year. While word leaks out from the Fred Davis camp that he won't take any sort of home town discount and wants to be one of the league's highest paid TE's averaging at least $7.5 million for the next 5-7 years.
The Redskins are scrambling as they can't afford (or should they justify) paying Davis that kinda money. Especially as they have very little maneuvering room against the cap next season. The Skins don't want to go back to Cerrato days of old where they just back load the contract, and they know that cutting Cooley won't be enough to get Davis under contract for next year. They don't want to lose Davis for nothing, so they work out a deal with the Bears, where they get Chicago's 2nd round pick in 2013, and a conditional 6th round pick in 2014, that can rise to a 4th rounder depending on how productive Davis is.
Now most teams wouldn't give up potentially a 2nd and 4th round pick for a one year rental (cough McNabb). But the Bears should very much be in the playoff hunt this year, and are desperate for a TE after dumping the Mike Martz system. The Bears have no one really to speak of at TE, and with Johnny Knox potentially out for the year, the Bears need another weapon opposite Brandon Marshall. They are definitely a team that could get desperate and pull the trigger.
As for the Skins, the loss of Davis could sting a little initially, but it is a far better outcome than losing him for nothing next offseason. If Cooley and Paul are productive the team shouldn't notice a major dropoff, especially with the increased receivers. There is no way the Skins could afford a mega deal to Davis at this time, especially since he's really only a pass catching TE. It would be tough for some fans to swallow, but adding a 2nd rounder and more, would help make up for the loss of draft picks.