Not really.
1. Besides the obvious Revis situation (which will likely either result in a $20M cap savings or a new deal with a $8-12M cap savings), the Pats have a lot of options to free up money in a hurry. Around $4M from a Mayo restructure, around $5M from shifting $7M of Brady's salary into signing bonus, around $4M from cutting Amendola with a post-June 1 designation, all according to Miguel. $1.2M from cutting Hooman. I wouldn't be surprised to see tweaks to deals for Vollmer, Browner and Arrington to free up money. Long term deals with Gostkowski and Solder would also save cap space, but will probably take more time. But I think the Pats have plenty of room to get under the cap.
2. Almost all of the signings being reported are big money deals with teams overpaying. 4 years/$36M for Orlando Franklin, 5 years/$44M for Rodney Hudson, 5 years/$45M for Jerry Hughes, $11M/year for Jeremy Maclin. The Pats aren't going to be pursing those kind of deals. Any of our own FAs (other than Revis, if he reaches FA) either won't go very quickly, or they will be gone because someone will be overpaying for them. Connolly, Branch and Casillas aren't going to break the bank. If Vereen and Ayers get big offers, they are gone. Most of the guys being discussed aren't going to break the bank, and if they do, they won't be a consideration for the Pats.
I personally think the Pats should be proactive to (1) get their house in order to free up cap space, (2) resolve the Revis situation, (3) monitor the FA market, and (4) identify potential external targets of interest and establish conversations with them through their agents to gauge interest and market range. I expect all of those things to settle within the next few days or the next week at the latest, and then I expect the Pats to be very active, whether it's re-signing players or signing new ones.