Failure from the Boks will badly hurt their fervent home support, and their team's next test is a potentially difficult one against a resurgent England at Twickenham in five weeks. Their coach Eddie Jones must be licking his lips in anticipation.
"We're playing against the world's best team, the No1 team, without a doubt," Coetzee said of the All Blacks. "They've had the best continuity in coaching structures and players. Like I've said previously, they have great systems. But our motivation comes from within. It's not external.
"People write us off and we want to show them? No, No. That's not how a Springbok operates.
"We understand the tradition of the rivalry between the All Blacks and South Africa... if you hear of the respect the All Blacks have for South Africa and vice versa you understand that we will be up for this game.
"For us yes... the game plan might not be finished by the end of 2016 but it's a work in progress. I'm looking for this team to go out and perform."
For that he will largely be relying on 32-year-old Steyn, the former Bulls hero who has been plying his trade at Stade Francais since 2013. With Lions star Jantjies out of favour and Pat Lambie and Handre Pollard injured, the Boks have had no choice but to turn back to Steyn.
For many it will be a retrograde step, but the Boks don't have the depth of the All Blacks - few teams do. Should the in-form Beauden Barrett be ruled out, coach Steve Hansen has Aaron Cruden, Lima Sopoaga or Damian McKenzie to turn to.
So now Coetzee is hoping Steyn can turn back the clock to that famous day at Kings Park seven years ago when his first-five scored all his team's points - a try, a conversion and eight penalties - in a 31-19 victory over the All Blacks.
"Morne Steyn has done a great job for us against Australia," Coetzee said. "He's been around the block. You're not going to change Morne Steyn to change his game per se, but he knows what's needed. He understands that at No10 we need to have sharp decisions, big decisions, without any unforced errors. He's been doing that."
The game, and the All Blacks, have moved on significantly since 2009. Another big victory will leave Coetzee and his men between two game plans and without the confidence to grasp either. This is an important test for South African rugby.