The New Orleans Saints are a surprising $3,604,470 under the salary cap as of today, according to the NFLPA's website. Which, to be quite honest, is way more than I would have guessed. Particularly after signing Nick Fairley to a one-year contract earlier this week.
Just this past Monday the team was listed as being a mere ~$230,000 under the cap. Obviously the recent restructuring of the Cam Jordan and Thomas Morstead contracts gave the Saints a little breathing room. And there is still room to free up more money if necessary. If they can get Max Unger to restructure and/or Drew Brees to agree to an extension, they'll have even more money. But with the free agency market nearly tapped out, they shouldn't need much more other than to sign their draft picks.