But another bad loss at home against a mediocre Springboks team, who have split their first two Tests with Argentina, would crank up pressure on them.
Cheika appears to be feeling the heat, if his post-match spray at referee Romain Poite - who he alleged ignored captain Stephen Moore and also had a secret meeting with the All Blacks, which counterpart Steve Hansen subsequently refuted - is anything to go by.
But he doesn't feel his position is in any jeopardy.
"I don't think I am (under pressure)," Cheika told reporters in Sydney.
"The only person who puts pressure on me is myself.
"I'm not worried about that stuff."
The Springboks were disappointing in a 26-24 defeat by the Pumas in Argentina on Saturday night and may present the Wallabies with an opportunity to play themselves back into form.
However, there is plenty of work to do.
Australia barely had a chance in attack in Wellington, running the ball 187m to New Zealand's 411m, and were held tryless as the rampant hosts crossed the white line four times en route to clinching the Bledisloe Cup for a 14th straight year.
With no injured players expected back for Brisbane, Cheika has already declared his intention to stick with Quade Cooper and Bernard Foley as the team's twin playmakers, while lock Adam Coleman brought some promising vigour in just his second Test appearance - if overdone at times.
Young backline utility Reece Hodge showed some signs in his debut off the bench, including kicking a monster 52m penalty, that suggest he could become a regular for years to come.
But apparent glaring problems remain, including lineout woes and a lack of ball-running forwards, especially a power No.8, to provide much-needed go-forward.
Vice-captain Michael Hooper believes, despite their two Bledisloe beltings, a win isn't too far away.
"We made huge improvements during the week," he said.
"Still the scoreboard didn't paint a great picture but as far as intent of the guys at training and in the game, you can't build that sort of stuff and not get results in the back end of the year.
"(I'm not) hoping, I'm knowing there's some good to come from this."
- AAP
