It won't happen this week. The Super Bowl-winning coach is ignoring those pleas to play it safe, again.
"There's no perfect way to do it, but having your guys rested and ready to go usually helps you," the Colts coach said.
Those around Indianapolis greet Dungy's sentiments with a sense of doom.
They remember 2005, when the Colts started 13-0 and essentially took a month off between meaningful games, then lost in the divisional round to eventual Super Bowl champion Pittsburgh. They recall playing Tennessee last year, in a similar situation for the regular-season finale, and then watching the Colts fall again in the divisional round, this time to San Diego.
Then they look at last season's New York Giants and how they played the starters in their finale against New England, a ploy many thought helped boost New York toward its Super Bowl upset of the Patriots.
But while the debate rages in Indy, Dungy is among the mainstream thinkers in his profession.
Tom Coughlin, whose Giants now hold the NFC's top seed, also is considering sitting some players this week. Titans coach Jeff Fisher, whose team has already locked up the AFC's top seed, may do the same.
Already out for the Titans (13-2) are Pro Bowl defensive tackle Albert Haynesworth (sprained left knee) and defensive end Kyle Vanden Bosch, who is recovering from groin surgery. Pro Bowl center Kevin Mawae may sit out, too, after hurting his right elbow last week against Pittsburgh.
That's not all. Quarterback Kerry Collins is expected to be pulled early.
"If there are players that are going to benefit from the rest or players that may benefit from playing a series or two, then so be it," Fisher said. "We're going to do our best to implement a game plan and have a chance to win, but again, we're going to keep in mind what's ahead."
In this case, that means vanilla game plans.
Sunday's game at Lucas Oil Stadium is the only matchup this week between two teams already locked into playoff position. And with a potential third meeting between the AFC South rivals, nobody wants to give away secrets.
Since their first meeting, a 31-21 Titans victory in October, Indianapolis (11-4) has won eight straight since facing the Titans and another win would extend the franchise's NFL record of consecutive 12-win seasons to six. The Titans, meanwhile, need another win to set the franchise record for single-season victories with 14.
There are personal incentives at stake, too.
Peyton Manning needs 93 yards to reach 4,000 this season, and tight end Dallas Clark is within 42 yards of breaking John Mackey's single-season record for most yards receiving by a tight end.
And the Colts want to avoid their first season sweep since 2002.
"I think it's important for us to go into the playoffs winning," Colts center Jeff Saturday said. "We want to beat Tennessee, especially since its a team you might face in the playoffs."
But on the 50th anniversary of the Colts 1958 championship victory over the Giants, a game that put the NFL on the national map, forgotten names will likely to dictate the outcome.
Backup quarterbacks Jim Sorgi and Vince Young are expected to play at least a half.
The Colts may start Joseph Addai but are likely to rely more on backup Chad Simpson, and receivers Marvin Harrison and Reggie Wayne will probably make early exits, too.
Tennessee is likely to follow suit with players like rookie running back Chris Johnson. Those who have been here, such as Titans safety Chris Hope, understand. Hope won a Super Bowl in 2005 with Pittsburgh.
"You have to be smart about it," he said. "You've already given yourself a chance to play in the next season. You have to go out and have a great week of practice and go out with the attitude of winning the game no matter what."
But Dungy believes the risk of losing timing and momentum versus the risk of injury is a no-brainer -- regardless of what others believe.
"Whatever you do, if you win it's the right thing and you were smart. If you don't win, you did the wrong thing and you are not very smart," Dungy said. "We are going to do what we think is best. We thought it was best then (in '05 and '07) and we think it's best now and, hopefully, we win and look smart at the end."