In both years they lost bad games to Washington in Week 15 (22-10 vs. 23-10) but that's not the most of it...
In 2007, the Giants started the playoffs by easily beating an NFC South (Bucs) team. Then they beat the No. 1 seed (Cowboys) on the road. Then they beat the No. 2 seed (Packers) in the conference title game when the opponent turned it over in overtime (A Farve INT) and gave the Giants a short field and the Giants won on a Lawrence Tynes overtime field goal. Then they moved on to face the Patriots in the Super Bowl.
In 2011 let's see....
NFC South (Falcons) - we kicked their ass.
No.1 Seed defeated (Packers)
No.2 Seed defeated after turnover in OT via Field Goal by Tynes. (49ers)
Patriots in Super Bowl.
Just have to beat the Pats to complete the unlikely chain of events a second time.