QB is currently 3 deep, so the most the team needs there is a camp arm.
RB is currently 5 deep, so the most the team needs there is camp depth
TE is currently 4 deep, so there's nobody needed there
WR is currently 6 deep, so a legitimate competitor and a longshot or two are needed
NT is currently 1 deep with pretenders, so backup NT is a need
DE is currently 1 deep with questionable competitors, so a signing here would be good
OLB is currently somewhere between 0-1.5 deep, depending upon how much you like Ninkovich and Cunningham. There's a definite need there
ILB is currently 2-4 deep, depending on how much you like the backups as all-around subs. The team should be ok here, but a plugger for competition wouldn't hurt
CB is fine if Bodden's 100%, McCourty doesn't have a sophomore slump and they can get nickel and dime performance out of one of the remnants (Dowling/Butler/Arrington/Wilhite). No signings are really needed unless the team wants more T.C. bodies
S is fine if they bring everyone back.
K should be fine if the rehab's gone well, although bringing in a leg to help with camp might be good
P should be fine, although bringing in a leg to help with camp might be good
LS should be fine
Taking a look at the roster and noting that it'll be a shortened offseason, it really seems as if the team would only need a few players as training camp depth, and a scant handful of legitimate competitors for jobs. That being the case, the team should be fine under the cap. Depending upon the final number, the Patriots might well have the money to look at a quality player at one or more of the OLB/WR/DE positions.*
* I didn't include the O-line because there's not enough info about the upcoming rules to make a really informed guess here. However, Miguel's already got Mankins under the cap with the team having money to spare, and Light's cost should be reasonable given his age, so I don't see a financial reason why he couldn't be brought back and still leave the team with spending money. Given the chance, I'd be all for the team making a run at Nicks. That would potentially result in an enormous future o-line of Solder/Nicks/Cannon/Vollmer/Center.