My thought process went along the lines of Hawkwow's. Sherman wants to be seen as the best CB in the NFL, and he will want to be paid accordingly, as that's part of the "respect" thing.
A couple of things could change this:
Seahawks could offer Sherman the largest contract ever, then Sherman would pull a Brady and take less than was offered. This appeases the respect issue, and also makes Sherm look even better for being a team player. Kind of fantastical, but I could see both sides orchestrating this beforehand. If a team goes out of it's way to make a player look this good to the rest of the league, it would probably appease that player's ego.
If Sherman gets repeated media and league accolades as the undisputed best CB in the NFL, then he might have his ego stroked enough to be amenable to a team friendly deal. After all, if it's common knowledge that he's the best, his contract wouldn't necessarily have to reflect that.
If Russell Wilson keeps going at his pace from the last half of last year (without much improvement, just keeping that level) he'll be considered a top 5 QB in the league and would command 16-18 million a year. I have no doubt about Wilson's character that he'll get paid well, but won't hold the Hawks' feet to the fire; he'll take a team friendly deal to not crush our salary cap.
From what I've read, Miller's contract is much more cap friendly after this year. Coincidentally, there are guys like Thomas and Sherman that will need to get paid. Gee, wonder if the FO did this on purpose ? Rice, on the other hand, might have to restructure.