EAST RUTHERFORD, N.J. — The focus of the New York pro football world on Sunday will be on Buffalo, where the jaunty Jets, in a surprise, chase a playoff berth that might lead the franchise to its first Super Bowl in 46 years.

But on the same day at MetLife Stadium in New Jersey, the atmosphere will be bittersweet as Giants fans could bid goodbye to Tom Coughlin, the persnickety old-school coach who twice led undervalued Giants teams to upset Super Bowl victories. With the Giants concluding their third consecutive losing season, the 69-year-old Coughlin — a doughty, arm-waving, immutable fixture of the team’s culture — appears poised to lose the job he has held since 2004. Coughlin may also choose to retire.

For Coughlin, raised in upstate New York and surrounded by Giants fans, it would very likely be the end of a 46-year coaching grind that has taken him and his family from a first job in Rochester to college and pro stops in Syracuse, Boston, Philadelphia, Green Bay, New York, Boston (again) and finally to N.F.L. head coaching positions in Jacksonville and with the Giants.