The only current NFC coaches who have won multiple Super Bowls are feeling positive about their futures despite poor 2013 seasons.
These teams finished first and second in the NFC East last year, with Washington (3-12) capturing its first division title since 1999.
Now the Redskins will finish last for the fifth time in six seasons as they try to avoid their worst record since 1994. A loss Sunday would also give them their first eight-game losing streak in more than a half-century, since they dropped 17 straight over the 1960 and 1961 seasons.
Speculation is rampant that Shanahan's fourth season with the club will be his last, but the two-time Super Bowl winner with Denver insists he wants to stay on. He will meet with owner Dan Snyder.
"I love these guys," Shanahan said. "And we've been working extremely hard to put this thing together, and we've had a couple of bumps, which we all know with the salary cap, but I'm looking forward to building this football team. But, like I said, it's a situation where I'll get a chance to sit down with Dan at the end of the season and we'll go from there."
Coughlin's two Super Bowls have been more recent with New York (6-9), which won it all just two seasons ago. The Giants will finish with their first losing season since going 6-10 in his first year in 2004.
New York has won six of nine since an 0-6 start, and Coughlin said this week that he wants to return.
"Sure, absolutely," Coughlin said. "I mean, probably even more because there are a lot of those that are telling you that you didn't do very well and you're not a very good coach and you're not this and you're not that, so perhaps you have something to prove."
The Giants are clearly finishing stronger than the Redskins, winning 23-20 in overtime at Detroit last Sunday to eliminate the Lions from playoff contention.
That victory came after back-to-back 23-point defeats that called into question how New York would finish the season even though Coughlin has insisted that pride was enough of a motivating factor.
"From my standpoint is we've been in a couple of celebratory locker rooms after Super Bowls," Coughlin said. "Well, how's it going to look if some of these guys were with us in the good times and it's not so good right now? How are we going to act? What is our statement about who we are? And what kind of example are we for the young people? So I think pride is very important."
Eli Manning has set a career high with a league-worst 26 interceptions. He'll again be without top receiver Victor Cruz, who is sidelined with a knee injury.
The Giants also do not know who will play at running back. Rookie Michael Cox could make his second start since Andre Brown and Peyton Hillis are both being treated for concussions.
New York won 24-17 at Washington on Dec. 1, but won't face Robert Griffin III this time around. Kirk Cousins will make his third straight start, fourth of his career and first against the Giants.
Cousins threw for 381 yards with three touchdowns and two interceptions in a 27-26 loss at Atlanta on Dec. 15. He was less effective in last Sunday's 24-23 home loss to Dallas, completing 21 of 36 passes for 197 yards, one touchdown and one interception.
"I think I'm in a good spot right now," Cousins said. "Obviously, we would have liked those be wins but we're two points away from being 2-0 in this three-game stretch and hopefully we can get a win this week."
Cousins will no doubt be targeting Pierre Garcon, who has been thrown to a league-leading 172 times and leads the NFL with a Redskins-record 107 catches. Garcon had nine receptions for 61 yards in the first meeting.
The Redskins have done a good job of protecting Cousins, who has been sacked once in his starts. New York sacked Griffin five times earlier this month, with Justin Tuck recording a career-best four.
Tuck, who has 7 1/2 sacks over his last five games, is one of several Giants who could be playing their last game with New York.
"I'm looking ahead," Tuck said. "Anytime you go into a season like this, you always take time out at the end of the year to go over the goods, the bads and the ugly. I'm looking forward to getting back to the top of the heap."
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