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Long time Australian back Matt Burke says sacking Cheika's assistants — the move many see as the most likely outcome — would not rescue the ailing Wallabies.
The former rugby pacesetters have won a paltry four from 13 tests this year, and won less than half their games since making the last World Cup final.
Veteran columnist Greg Growden has led the charge against Cheika and also slammed Rugby Australia this week for procrastination and keeping fans in the dark.
Burke has followed suit, with chairman Cameron Clyne, chief executive Raelene Castle and the Rugby Australia board in his sights.
"Michael Cheika after that [season] has to go ... [it has] been so poor from the Wallabies' perspective," Burke said on the Big Sports Breakfast radio programme..
"There has to be a change. I don't think just getting rid of the assistant coaches will be enough. I think they have to change it from the top down. Getting rid of the assistant coaches won't be enough because it's still the same voice.
"At the moment it's untenable when you're looking at the situation from the coaches and then the high performance managers and the rest of it."
He acknowledged Cheika's record in Europe, Super Rugby and the 2015 World Cup showed he did have coaching credibility.
"...but when you look at some of their performances out on the park there you think 'well are you really playing for your coach?'
"The players have to be accountable and that is the hard part about it."
Clyne has been derided for what has been described as a "comical" 50 second press conference when he refused to take questions about Cheika's position. RA will make a decision on the coach before Christmas.
Burke, an 81-test World Cup winner, said: "I would have thought they would go all through the night, work it out and come and make a statement and tell him whether you're in, or whether you're out.
"The rugby brand in itself is struggling, no doubt about that. The way they're losing, the brand is being damaged incredibly at the moment. If you were talking in a business sense, and a CEO was performing like that, you would out him straight away.
"They're floundering off the field, they're floundering on the field. I don't think Cameron Clyne has endorsed himself again even after the Western Force saga. [There are] question marks over the chairman for sure.
"They need to make a call. They are sitting on their hands."
The Sydney Morning Herald reported there were "influential figures in rugby land, however, who believe the board is well within its rights to take its time" over the coaching situation.