Who are these other above average QB available? Vick?
Even if Cutler won't go for the Bears deal, they'll tag him, mark it down.
The Bears don't want to tag Jay because of the cost to the cap, and Jay doesn't want to be tagged because he misses out on a lot of long term guaranteed money that he could lose with one injury in that situation. QB's just don't get tagged these days, there really isn't an incentive for it on either side.
The Bears will likely re-sign Cutler, unless their number is an insulting lowball offer that forces him out of town. I don't see them doing that as an organization. Cutler seems to like everything about his current situation, as well as other key guys--like Brandon Marshall, which is going to be a consideration. Will the Bears overpay? Likely. When guys like Matt Schaub and Matt Flynn get inflated deals it forces the market higher for proven vets like Jay. But Jay has an injury history that would deter most teams from throwing ridiculous money his way as well. I figure he'll get 4 years and around $70 million, which would be very manageable for the Bears given their cap position.
The Bears want to get his deal done and out of the way soon, since his is the biggest piece of their off season acquisition work. They need to know where his number is at long before the free agency period opens in March. That will probably cost them some money to get done, but it is in their best interest to do it.
Letting Cutler walk in March is just a huge risk to the team, and to Cutler, too. I don't think it ever gets that far.