If this happens, I can see some potential parallels with Ray Allen. A guy who has been a very productive player but feels underappreciated and thinks he hasn't been given the security he deserves, and then departs to leave for a rival.
Speaking as a regular Joe who's never made big bucks, I still fail to see how $7-9M a year (the range in which the Pats' offer to Welker is believed to be) isn't enough "security," or enough to "take care of your family." So I think the Welker situation is more about how valued he feels.
The way I see it, if you like the coach you play for, the teammates you play with, and you're getting paid millions, why look anywhere else?
Does Welker feel slighted? Is that the problem? Sure, he's taken some heat for dropped passes, but I think the New England fan base generally loves and appreciates him. Brady wants him to stay. I'm sure Belichick does too. So what's the problem?