Australia appears set to get its sixth change of prime minister in 11 years today in a ballot of government lawmakers which would continue an era of extraordinary political instability.

Foreign Minister Julie Bishop is among the favourites and would be Australia's second female prime minister. Other favourites include Treasurer Scott Morrison and the only declared challenger Peter Dutton, a former Cabinet minister.

Beleaguered Prime Minister Malcolm Turnbull demanded the names of lawmakers in the conservative Liberal Party who wanted him to go before he would allow them to choose a new prime minister at a meeting at Parliament House today. The names would provide proof that a majority of his government had abandoned him.

Turnbull would then become the fourth prime minister to be dumped by his or her own party before serving a full three-year term since the revolving door to the prime minister's office started in 2010. The trend is universally hated by Australians.

"Australians will be rightly appalled by what they're witnessing," Turnbull said yesterday in announcing the meeting that would end his career. Public anger became apparent overnight with windows broken at the Brisbane office of Dutton, Turnbull's main rival in his government.

Dutton has told the prime minister that a majority of Liberal Party lawmakers at least 43 don't support his leadership. But Dutton's supporters yesterday could not find 43 lawmakers prepared to sign their names to a petition demanding a leadership ballot.

An explanation could be that some lawmakers fear they will be punished by voters if they put their names to dumping Turnbull. The ballot to choose a prime minister is secret, so lawmakers don't have to declare which candidate they voted for. Many later lie that they backed the winner.

Support for ousting Turnbull might also have waned because he warned yesterday he would quit politics rather than ask his party again for its support in a ballot. His resignation from Parliament would force a by-election that could cost the government its single-seat majority. The resignation could also push his successor into immediately calling general elections.

Mathias Cormann, a former Turnbull supporter who switched his allegiance to Dutton, said he was confident that the meeting would go ahead today. He declined to say how many signatures had been collected.

The party's federal executive had intervened, telling a defiant Turnbull but that the state branches unanimously wanted the leadership crisis resolved today, lawmaker Eric Abetz said.

Some lawmakers who were against the change of prime minister said they had agreed to sign the petition in a bid to end the impasse. "I am being pressured -- beyond any comprehension -- I am being pressured to put my name on that list so it can bring the party room to a meeting," staunch Turnbull supporter Scott Buchholz said today.

Turnbull had defeated Dutton 48-35 in a surprise vote on Tuesday. Turnbull initiated the ballot in the hope of ending speculation that his government had lost faith in him in the face of poor opinion polling. Several ministers have since resigned and told him that most of the government wanted a new leader.