I kind of feel like this is much ado about nothing. I like Butler and I wish him a productive career no matter what uniform he ends up wearing in four years.
For now, though, I think the Patriots have all the leverage.
Butler signed a three year contract in 2014 for $1,500,000. This is the last year of his contract and he is due to earn $600,000. He is a restricted free agent next year. Is someone who has earned about $1 million dollars walking away from $600,000? And even if worst case scenario he sits out this year, what does that gain him?
In 2017 he will be a restricted free agent which means the Patriots can keep him through the application of a tender. Let's assume that a first round tender means Butler will get a $4 million one year contract.
In 2018 the Patriots could then use the franchise tag on him. I agree that this is an extreme option but the simple fact is that the Patriots have the leverage to keep Butler on their team through the next three years (including this year). For 2016 a franchise tag on a cornerback would mean a $14 million dollar one year contract.
So, altogether, Butler could potentially earn about $19 million over the next three years. Of course, only $600 thousand of that will be earned this year and he is exposed to serious injury risk. If he gets hurt this year, he could be out a lot of money. I can't blame the guy for sitting out of optional team activities when it represents such a significant risk.
To extend Butler now, I think something in the ballpark of 4 years/$20 million gets the job done. For Butler this lessens his injury risk and it provides him with more of his projected income this year while also still allowing him to hit free agency (big payout) when he is 30 years old. For the Patriots, this type of extension allows them to lock in a key piece of their team for an extra year, it makes the player happy (happier at least), and it allows them to more evenly spread the cap hit for his projected salary over multiple years.
Relevant links:
http://profootballtalk.nbcsports.com/2016/03/08/nfl-sets-restricted-free-agency-tenders-for-2016/
http://www.cbssports.com/nfl/eye-on-football/25499237/here-are-the-2016-nfl-franchise-tag-and-transition-tag-numbers-for-every-position