When the 2010 season became an uncapped year, it meant that teams could front load multi-year contracts and take a smaller salary cap hit in the future. The Green Bay Packers took advantage of those rules on at least three contracts. But some teams did the opposite and had a significantly lower payroll. Since there was no salary cap floor either, they didn't have to spend a minimum on players.
Under the expected terms of the new CBA there appears to be a more significant salary floor which would leave a number of teams are under it. I was expecting some teams would be forced to sign some players when free agency begins, but Andrew Brandt says those new rules don't kick in for another year. From the National Football Post:
The NFLPA appears to have achieved this important gain. Teams now have a "guaranteed spend" in cash of 99% of the Cap on a league-wide basis, meaning they must collectively spend approximately $3.8 billion (higher in future years) with hard cash.
It’s important to note that spending is calculated at the end, not the beginning, of the year, so teams don’t need a free agent shopping spree to meet their requirement; they can do so by resigning core players throughout the season.