With dismal ratings in opinion polls and a backbench disgruntled by policy backflips, two of Abbott's MPs have said they will call for a challenge to his stewardship of the nation at a meeting of the governing Liberal Party on Tuesday.
But the conservative leader said he was expecting the so-called "spill motion", aimed at removing him and deputy Julie Bishop from their positions, to fail.
"Should this spill motion be defeated, as I expect, I will be taking that as a strong endorsement of the existing leadership team, as a vote of confidence in the existing leadership team," Abbott told reporters.
Labor switched prime ministers twice in their last turn in government, first in 2010 when Julia Gillard removed prime minister Kevin Rudd in a party room coup, and then in 2013 when they changed back to Rudd.
"We are not Labor... And this "Game of Thrones" circus which the Labor Party gave us is never going to be reproduced by this coalition," Abbott said in reference to the medieval fantasy drama in which characters vie for power.
But he said the "spill" motion, which if successful would remove him and Bishop from their roles and trigger a new vote among Liberal Party parliamentarians for those positions, would likely fail.
So far no one has stepped forward to contest the leadership should the backbenchers succeed in their push for a vote, likely to be decided in a secret ballot.
Communications Minister Malcolm Turnbull, a millionaire former lawyer who supports Australia becoming a republic, is considered a front runner while Bishop could also throw her hat into the ring.
"My role as deputy is to support the leader, not to change the leader and I don't support a spill motion," she said.
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