Cooper, for all of his skill when he is in form, has a tendency to fold under pressure, and the spotlight during the week and on the pitch is likely to be relentless as the All Blacks look to wrap the Bledisloe Cup up for the 14th year in succession.
Australia, for all their talent on paper, are a team of compromises. Cheika doesn't have a specialist No8 so he is forced to play David Pocock there.
Pocock was one of the better Wallabies on the night but his relative lack of height, combined with the short Michael Hooper, means the Wallabies are disadvantaged in the lineout, and that was a big problem area on Saturday.
Hooker and captain Stephen Moore must take responsibility for the performance of that set piece, plus the fact that he cannot last 80 minutes. On Saturday, like in the three tests against England, he left the field after 60 minutes.
Will Genia hasn't played a match since January but is by far the Wallabies' best halfback. How will he recover, physically and mentally, from such a beating?
How does Cheika get more use out of fullback Israel Folau? By playing him in the midfield, thereby leaving the Wallabies more vulnerable at the back?
These are the questions that Cheika must get to grips with this week as he attempts to salvage something from a year which is already getting away from him; the empty seats at ANZ Stadium were a testament to the fact that the Australian public didn't have a lot of faith in their team and he has already admitted winning back the support of rugby union fans is a big part of his job.
After the test he took responsibility for what he described as his team's poor mental preparation.
"I don't think it's about changing everything, it's about getting the focus clearly on what's important," Cheika said.
"I take responsibility for that, the mental preparation, that's my domain and I've got to make sure the players are switched on to what is in focus.
"And that's why you would see me being very down, because I feel like I've let them down because I haven't put them into a space where they're going to do whatever it takes, especially around defence.
"It's all connected, so I will have a good look at how I've prepared that over the last few weeks and try to add or refine and put some focus on what I need to make sure that the point is very clear for next weekend."