DMac's signing is a good example of the Pats strategy of NOT bidding against themselves. Although it would seem very risky to allow their key FA's to essentially get to FA (the legal tampering period is pretty much the first step into the FA period.). I believe the Pats found quickly found out that McCourty's market price was higher than they expected. My guess they put a price in the range of $8-8.5zMM/yr on him. Once they got a look at the market they upped that offer, and McCourty took it, even though he reportedly left some money on the table from other teams.
The Pats made their offer close enough to the market so that it was easier for McCourty make the "right" decision. For some players money isn't the only consideration in a contract negotiation. When considering the Pats the negatives are you probably won't get the last dollar, and they will work your ass off. But the positives are you will get to play in a great atmosphere, and locker room, improve your game with great coaching, and win. Most of the time, whatever dollars you loose in your contract, you can make up long term in playoff payouts, and off the field financial considerations.
Now as the focus turn to Revis, I expect a similar pattern to emerge. However I wonder if the competitive market for Revis will be a vigorous as DMac's. How many teams are willing to overpay (over $1hMM+/yr) for a 30 year old, albeit elite, CB. I don't think there are too many. In fact the reports are only the Jets seem ready to pull that trigger.
If that's the case, I'm also pretty sure that the Pats' best offer is going to be similar to the Sherman contract at $14MM/yr. I also think that will be enough to bring Revis back when he considers all the other positives resigning here will bring to his brand.
It should also be noted that while the Pats rarely pay "top dollar" they are usually "in the ball park" with their offers.