Sometimes, it's okay to pay a little extra for a guy if you know he's gonna help you win, and help you get the Lombardi.
Understanding that your context is a bit different:
Recent big money pacts have been given to Brady, Gronkowski, Hernandez, Mankins, Welker (both in the form of the tag at 9.6m and a likely new deal), Wilfork, and Mayo. I'm not seeing as much cheapness as some would claim, just the fact that they tend to reward players from their own system, and do not gamble as much with outsiders unless they are reasonably priced or in a tier of their own talent wise.
As far as FA goes, Belichick is likely going to continue his philosophy of assessing each player's value in his own specific way. In other words, he's always going to place value very highly, and not make any moves of a gambler's desparation.
I think we'll see the needs addressed, and they should be able to compete pretty well in free agency, even if it isn't necessarily a top notch player and more likely a couple of middle tiered players + some vets.
One thing's for sure, they will be spending to the cap, so that money will go somewhere.