Both teams also know that their respective 1-2 starts won't cut it if the NFC East-leading Philadelphia Eagles are going to keep coming from behind to win every game.
So never mind the fact that no one seems to like the idea of playing a Thursday night game, or that Redskins coach Jay Gruden joked that he was ''jittery'' this week because of the ''17 cups of coffee'' he had consumed just to accommodate the cramped preparation schedule.
Neither team can afford to coast through this one and fall 2 1/2 games off the pace.
''You fall too far behind the 8-ball this early in the season, it's going to be tough sledding,'' Gruden said, ''and we're already behind the 8-ball at 1-2.''
New York defensive end Mathias Kiwanuka said the first thing coach Tom Coughlin said upon walking into the meeting room this week was: ''In the division, in the division, in the division.''
The Giants, who started 0-2 before beating the Houston Texans on Sunday, are playing their first NFC East game of the season.
''We didn't start the season the way we wanted to,'' said New York's Eli Manning, who has struggled to find a comfort zone with first-year offensive coordinator Ben McAdoo's playbook.
''But we've got a chance to get back on track and get even and hopefully get something going.''
Time to get going, indeed, with some things to notice when the old rivals meet for the 165th time:
PUMELLED AND BRUISED: The Redskins listed 17 players on their injury report this week, including some who would have a much better chance at playing - or playing well - if the game were on a Sunday. The Giants aren't quite as battered, but they have the extra burden of travel: Road teams are 0-3 on Thursdays this season.
''You're talking about moving from the emotion of the game you just played right into your preparation,'' Coughlin said. ''And, of course, you have got to be a pro about that because it is mental, and you can't leave a stone unturned.''
ELI & KIRK, PROGRESSING: Manning finally made some headway under McAdoo's scheme with a 21-for-28 day against the Texans, while Washington's Kirk Cousins has posted a 105.8 rating in roughly seven quarters since taking over for Robert Griffin III (dislocated ankle). Cousins, of course, is miles behind Manning in intangibles such as experience and playing under pressure: He is 1-4 as a starter, and his career fourth-quarter rating is 59.3 after he faded late in Sunday's 37-34 loss to the Eagles.
''You don't like how we finished in crunch time, how I finished in crunch time,'' Cousins said. ''But, we'll learn from it and get better.''
SAFETY VALVES: Manning and Cousins might want to take a peek downfield more often than usual. Free safety has been a problem for both teams.
The Giants benched Stevie Brown after he was beaten for a touchdown pass against the Texans and replaced him with rookie Nat Berhe. Quintin Demps appears set to start Thursday after practicing with the first unit this week.
The Redskins cut Bacarri Rambo after he allowed big plays in the first two games while Brandon Meriweather was suspended. Meriweather is back, but he looked out of sorts against the Eagles. Another would-be option, Duke Ihenacho, broke his left foot and is done for the year, further depleting a secondary that has also lost cornerback DeAngelo Hall (ruptured Achilles) and will start rookie fourth-round pick Bashaud Breeland against the Giants.
SPECIAL FIXES: If nothing else, both teams would have appreciated a full week to work on special teams. The Giants botched a short field goal attempt and were fooled by a fake punt against the Titans, while the Redskins allowed a kickoff return for a touchdown and had a short field goal attempt hit an upright against the Eagles.
''There is definitely going to be some competition and a lot of talking going on,'' Giants cornerback Rodgers-Cromartie said. ''He likes to go deep, so you have to have on your good shoes.''
Jackson said his friend is one of the few defenders who can keep up.
''At the end of the day, he still has to be able to guard me,'' the Redskins wideout said, ''regardless of how fast you are.''
AP NFL websites: www.pro32.ap.org and www.twitter.com/AP-NFL
Follow Joseph White on Twitter: http://twitter.com/JGWhiteAP