Scott Morrison faces potential chaos in his first week in parliament as prime minister, with Labor determined to test his fragile majority.
The deputies of the Senate are also dissatisfied with their decision to abandon the National Energy Guarantee and the tax cuts to companies.
The departure of Malcolm Turnbull has stripped the government of its majority of one seat.
If all the deputies of the lower house vote in the same way as the Labor Party, the votes will be even, and the president will be forced to vote for the tie-breaker.
Labor is expected to play in chaos by seeking to refer Peter Dutton to the High Court, with the Greens to move a motion of no confidence in the Interior Minister.
"I think anyone who wants to predict how this week is going to be is very brave," labor leader Tony Burke told ABC radio on Monday.
Independent Senator Derryn Hinch said the coalition has spent a year trying to convince the coalition of the merits of its energy and tax policies.
"I'm not sure if it's worth it," he told Seven Network.
Senator Hinch said he had spent "hours and hours" telling him why the National Energy Guarantee was so important.
"The NEG is dead, I've spent hours with Mathias Cormann in taxes on the company, and that's gone," he told ABC.
"I should go to Christian Porter and say, 'Why am I talking to you?', This (Family Court legislation) could be out of discussion next week."
The latest Newspoll shows that the coalition behind the workers 44 to 56 percent on two-part preferred terms.
"We have a government here now … that is divided, that is illegitimate, that does not know why it is there, and you bet that we do it," Burke said.
Finance Minister Mathias Cormann said the government focused on the issues that matter to voters.
"The Labor Party always performs acrobatics," Senator Cormann told reporters at the House of Parliament.
Dutton, who failed in his bid to become prime minister on August 24, is expected to be pressured on two fronts: the issue of the au pair visa and his eligibility to sit in parliament on the interests of his care center childish.
Burke argued that Mr. Dutton should refer to the Superior Court after having "confused the parliament" and supports a motion of distrust in him.
Four parliamentarians, including treasurer Josh Frydenberg, will not be in parliament as they take time to commemorate Rosh Hashanah, the Jewish New Year.
"Take your hand"
Environmental activists have scaled the towering antlers out of Parliament in Canberra, displaying a huge banner condemning the coal industry.
Two Greenpeace protesters blew up the bright yellow banner that showed an image of Prime Minister Scott Morrison holding a piece of coal along with the words "take my hand."
"On the first day of Scott Morrison as prime minister in Canberra, we let him know how we feel about his comfort with the coal industry through a banner outside of Parliament," the green group posted on Twitter.
Meanwhile, farmers and their supporters are holding a demonstration in Canberra to demand that the federal government take urgent action on climate change.
A convoy with farm dogs made its way into State Circle on Monday morning before the speakers addressed the crowd.
"Rural Australia is at the forefront of climate change, and although our politicians have wavered for a decade, we have grappled with the harsh realities of inaction," said Farmers for Climate Action director Verity Morgan-Schmidt.