Clemson (6-5, 4-4 ACC) claimed the school's first-ever ACC Atlantic title last season, and had Georgia Tech in the championship the following week. South Carolina (8-3, 5-3 SEC) will represent the East in next week's conference championship against Auburn.
Swinney doesn't see much reason to move the Clemson/South Carolina game, at the expense of a game that's scheduled for the following week.
"That's a huge game for everybody. It always will be," he said. "Hopefully we'll be able to win our division again and go back into it as division champs. There may come a day where we're both division champs going into this game.
"This game is huge. It's a big deal for both programs—the state and everybody involved. If you've got a game next week, it really shouldn't matter. It's all about this ball game, right here."
Swinney also acknowledged Sunday there's a difference in the two marquee rivalries in South Carolina and Alabama.
"I think it's a little bit of a difference, from a national standpoint," he said. "There were many times [Alabama] had the division won, but [the Auburn game] was just as big."
After the 30-10 win over Wake Forest, Clemson and South Carolina were scheduled to play next weekend's game on ESPN2 at 7 p.m.
The win over the Demon Deacons also made Tigers bowl eligible for the 12th consecutive season.
Clemson head coach Dabo Swinney is 1-1 against South Carolina's Steve Spurrier. (Getty Images)
"To go from where we were the week before, to going up there and beating them by the largest margin of victory since '78, that's a good compliment to the character of our team, and a great job our staff did," Swinney said. "We're happy to be bowl eligible."
Clemson will try to build on that mark against a South Carolina team that's put up big numbers with QB Stephen Garcia, RB Marcus Lattimore and WR Alshon Jeffery.
"They're probably the most balanced team—as far as being able to make big plays—that we've played," Swinney said. "We've just got to do a good job ourselves—on offense—of taking care of the ball and score touchdowns. That's the biggest thing. We've got to score touchdowns."
ELLINGTON UPDATE: Running back Andre Ellington's status for the game won't be known until Tuesday.
"He's continued to get better since I saw him on Thursday," Swinney said. "Hopefully, he'll be ready to give it a go. I won't really know until tomorrow night or Tuesday morning, where he is."
Ellington has missed the last three games with a foot injury.
In eight games this season, he's rushed for 686 yards and 10 touchdowns while 17 runs of 10 yards or longer.