The Springboks have left behind 20 players from their regular squad, but White claims his team are nevertheless eyeing an upset.
"What is going to happen if this Springbok team beats the All Blacks?" White asked a stunned media conference.
"It will be a national disaster in this country, let's be honest. We have already seen how an All Black team that did not believe it would lose to the Wallabies in Melbourne did just that.
"This kind of thing does happen in rugby union. That is why it is such a fascinating game.
"And if they do lose to this Springbok team, can you imagine the psychological high South Africa will take into the World Cup and the corresponding low for New Zealand?"
White claims he is fielding a young team in Christchurch in order to increase the depth in South African rugby.
"The bottom line is that to win a World Cup you need a squad of 30 good players, a squad of top-quality depth," White said.
"That is what we are trying to achieve. New Zealand have already done it.
"Their biggest strength is that they have so many great players. Last year, two completely different All Black teams played Scotland and Ireland on consecutive weekends.
"Should we now interpret that as disrespect for Scotland and Ireland?" he asked.
"Why when we do it are we insulting people?
"If Carl Hayman, Richie McCaw or Dan Carter got injured on Saturday, is that the end of the All Blacks' World Cup campaign?
"Would England have won the World Cup if Martin Johnson and Jonny Wilkinson had got injured? Who knows?
"But what I do know is that we do not want to take chances.
"People must understand that when you are going into a World Cup year, you don't want to be saying to yourself 'what if'. You have to make sure you have enough back-up.
"And that is why people are making too much of this 'B' and 'C' side stuff.
"The reality is that the strength of New Zealand rugby is that they long ago made sure they had 30 players who could play in the World Cup, and they did that by interchanging players regularly on tours."