I'm not a big fan of chasing the big names, but you're not 100% correct.
who do the pats have under contract beyond 2014? mankins, mayo, solder?
who else?
on top of that, the cap is going up substantially at that point. they're going to have to pay somebody
I doubt there are very many players throughout the entire NFL signed beyond 2014. Regardless, here is the Patriots contract situation in regards to when contracts will expire for players that they have that are currently under contract. In addition there are the restricted free agents that were tendered (Hoyer, Love), and the player designated with a franchise tag (Welker).
Expiring after 2012: Light, Waters, Arrington, Woodhead, Brace, Chung, Barrett, Vollmer, Polite, Thomas, Edelman, Underwood, Pryor, Fletcher, McDonald, Kopa, Ventrone, Davis, Moore, M Carter, Rivera, Lavarias, Hix, Kettani, Silvestro, Cox, Hartline
Expiring after 2013: Ochocinco, Ninkovich, Gronkowski, Wendell, Cunningham, Hernadez, Spikes, Mesko, Deaderick, Brown, Aiken, Tarpinian, Williams
Expiring after 2014: Brady, Wilfork, Gostkowski, Solder, McCourty, Dowling, Vereen, Ridley, Mallett, Cannon
Expiring in 2015: none
Expiring in 2016: Mankins
Expiring in 2017: Mayo