Already, the Wallabies' three-from-nine success rate in 2016 is their worst since Jones was sacked after coaching the national team to just five wins from 13 Tests in 2005.
Cheika is under no such pressure, having re-signed this year until the end of the 2019 World Cup in Japan.
But the reigning international coach of the year is certainly eager to reverse his side's fortunes, having guided Australia to last year's World Cup final in a memorable 2015 campaign that yielded 10 wins against just two losses - both to the All Blacks.
The Wallabies, though, know full well they face a mammoth task ending an infamous 30-year losing streak against the All Blacks at Eden Park, where the All Blacks haven't been beaten by any opposition in 36 Tests stretching back to 1994.
"That's a fair few generations of Wallabies and we have the opportunity," said Wallabies' returning back-row star David Pocock.
"We know it's going to be tough so we're preparing well this week and going over and playing the No.1 team in the world, we expect it to be a tough Test match and no doubt it will be just that."
Pocock expects no complacency from the All Blacks, despite their having already clinched the Bledisloe Cup for a 14th straight year.
Nor does he suspect their trans-Tasman rivals to be feeling the pressure of trying to claim a world-record 18th consecutive Test victory.
Instead he is challenging the Wallabies to match the All Blacks for skill and intensity for the entire 80 minutes after "we were found wanting" in both areas in Sydney and Wellington.
"In those big games, particularly against teams like New Zealand, you drop off for 10 minutes and that's the game," Pocock said.
Cheika will name his team on Thursday afternoon before flying to Auckland.