EAST RUTHERFORD, N.J. — The showboating Yankees may win more often, but the staid New York Football Giants have quietly produced consistent teams and a handful of championships, staking a worthy claim as the city’s most revered franchise. Owned by the same family since its founding in 1925 as one of the N.F.L.’s earliest members, the team is like a regal trans-Atlantic ocean liner that rarely strays off course.

Until, that is, this year.

The Giants, who in 2012 won the last championship for a major professional sports franchise in the New York area, have ignominiously run aground with a 1-5 record and look far from ending that six-year title drought.

Fans now loudly accuse the Giants’ brain trust of not only bungling this season but ruining the team’s future, too.

At the center of it all is Eli Manning, the beloved quarterback who brought the team its last two championships, winning the Most Valuable Player Award in each Super Bowl, but who is well past his prime.