Not because the game will be broadcast to a national television audience. And not because people are beginning to ask on a regular basis why San Francisco's prized rookie - the seventh player selected overall in the June draft - has yet to record a quarterback sack as a 49er. No, Carter's extra motivation will be on the opposite sideline. That's where his father, Rubin, will be working Monday night - as the Jets' defensive line coach.
"It's going to be fun," Andre Carter said of his dad being the enemy for an evening. "It just puts a feeling in my mind that I'm going to have to get after it a little bit more."
Carter probably has that feeling already. Considered perhaps the premier pass rusher in the college draft this year, Carter has yet to record a sack in San Francisco's first two regular-season games - or the four exhibition games that preceded it. Some observers who expected more are getting frustrated. But Carter says he isn't.
"Never," he said. "Never. I'm playing against some great offensive tackles and I feel that each week I'm getting better, I'm improving. I think a lot of it has to just do with technique. Me and (Niners defensive line coach) Dwaine Board have discussed what I need to do to get better week by week. So it's a progression stage. It's not frustration."
Carter also has had similar discussions with his father, a former star nose tackle with the Denver Broncos' "Orange Crush" defense who has helped nurture Andre through all stages of his football career. Father and son talk all the time.
"He's told me he's getting better," Rubin Carter said this week. "He said, 'I'm getting close, dad. Each and every week, I'm getting a lot closer. I'm learning on every rep.' He feels every play he's out there he's becoming more aware mentally of what's going on around him, which is good. You've got to make the most of your opportunities on the field."
Monday will be an opportunity for Carter to make the most of his for the Niners - and in front of his father. "It'll be a unique situation to be able to look across the field and see my son," Rubin Carter said. "I'm certain he's excited about the opportunity to be across from me. Hopefully, I'll be on the sideline talking to my defensive linemen to try to get them to make more sacks than he does."