But the reality is the Jets were a talented team back in the late 1960s -- and the Giants share many of their qualities. A strong running game. A staunch defense. And a player willing to guarantee a win (wide receiver Plaxico Burress, although he began to backtrack later in the week, perhaps hoping to mitigate the bulletin-board material he had produced).
And just like the Patriots of 2001, these Giants thrive on the unity, mental toughness and bone-rattling style of play that has made the Pats so dangerous.
"The overwhelming image I have of us back in 2001 is that we didn't care what the oddsmakers or anybody else said about us," Patriots inside linebacker Tedy Bruschi said. "It was an us-against-the-world mentality. I see a little bit of the similarities between [New York's] mentality and ours back in 2001. But there's also a big difference, because that team won a world championship. That's something [the Giants] will be trying to accomplish on Sunday."
Plaxico Burress predicted a 23-17 Giants win, although he later said that was for entertainment purposes only.
While some Patriots acknowledge they would rather avoid talking about the opportunity to become the first 19-0 team in league history -- "You don't want to jinx yourself, because none of this really means anything if we don't play well," left tackle Matt Light said -- the Giants have proved to be the looser team this week.
During their final media session Thursday morning, cornerback Sam Madison spent part of his time filming his teammates' interviews. A few tables away, a handful of younger players started a game of spades that attracted a flock of reporters. Even Burress shrugged off his controversial prediction of a 23-17 Giants win.
"Every time I say something," he said, "I seem to make news."
The Giants, by the way, say this type of joviality is nothing new. It's part of a mentality fostered by formerly pedantic coach Tom Coughlin, who has changed so much that McKenzie said, "He's right in there joking with us these days."
Added defensive end Justin Tuck: "This is our personality. We have a good bunch of guys, and we don't put a lot of emphasis on the spectacle of the Super Bowl. Part of the reason is that a lot of us are young and naïve and this is our first time here. But we also know there's a time to have a fun and a time to get serious.
"We know we have to be ready on Sunday, because the other team is going to come to play."
The Giants understand there are no mysteries about what they have to do. They must pressure Brady, who threw for 356 yards and two touchdowns against them in a 38-35 Patriots win in the regular-season finale. They must contain wide receiver Randy Moss, who killed them with six receptions for 100 yards and two big scores (including a back-breaking 65-yarder).
The Giants also can't beat themselves. The Patriots thrive on opponents' mistakes, and the turning point in that first meeting was a critical second-half interception thrown by Giants quarterback Eli Manning that helped New England erase a 12-point deficit. Manning, by the way, hasn't thrown an interception since then.
New York's mind-set is just as important. Before the club left for Phoenix, defensive end Michael Strahan spoke to his teammates about how essential focus and pacing would be in the days leading up to the Super Bowl.