...for the Pats to go undefeated in the regular season, I think it might be the Giants who could be resting players. If the Giants beat the Skins and Bills (definite possibility), they'd have the 5 seed nailed down and would want to get rested and healthy for the playoffs. The Pats (if they beat the jets and Miami) would have a bye week to get healthy anyway.
With a NY Giant win, and a Minnesota loss this next week, the Giants will have secured the #5 seed, and could rest their starters for the final two weeks of the regular season to get ready and healthy for the wildcard matchup (probably Tampa Bay). It's highly likely they'll do just that, too. There's no reason for them to risk not only injury, but even fatigue, playing starters against the Patriots.
Belichick's history has shown that if he has a bye week, he'll play his starters deep into the game, if they do not have the bye week, he'll get his starters some rest.