The New York Giants are the first team with a four-game losing streak during the season to make it to the Super Bowl, since the 2002 Oakland Raiders. No other team in American football's Super Bowl era (beginning with the 1966 season) has lost four straight and made it all the way to the title game in the same season.
I find it very surprising that a team with four straight losses during a 16-game season could make the Super Bowl, for two reasons. First, because the season is so short, it doesn't give teams much time to recover and compile a playoff-worthy record (although it is possible to make the playoffs with a weak record). Second, if a team loses four straight, one has to wonder how good that team really is. A lot of Super Bowl teams didn't even lose four games the entire season!
In fairness to New York, the four straight losses were to three eventual playoff teams and a fourth team (Philadelphia), which was good in spurts. Plus, the losses were mostly close. The Giants lost on November 13 to San Francisco (27-20), Nov. 20 to Philadelphia (17-10), Nov. 28 to New Orleans (49-24), and December 4 to Green Bay (38-35). In the playoffs, however, the Giants avenged their losses to the Packers and 49ers. (Click here for the Giants' 2011-12 game-by-game log.)
Interestingly, the Giants played their upcoming Super Bowl opponent, the New England Patriots, during the season. New York won that game, 24-20 on Nov. 6, and immediately went into its four-game skid!
Looking at this all-time chart of Super Bowl teams (with won/loss records during the season and links to game-by-game logs), we see that a few teams during the past decade nearly lost four straight the season they made the Super Bowl. The 2005 Pittsburgh Steelers and 2003 Carolina Panthers each lost three straight, whereas the 2008 Arizona Cardinals lost four out of five.
In 1978, the NFL adopted a 16-game schedule to replace the previous 14-game docket. Also, prior to 1978 there was only one wild-card playoff team per conference, making it extremely unlikely that a team with four consecutive losses could even make the playoffs.