Prime Minister Tony Abbott is set to test Labor's post-election resolve to block the carbon and mining tax repeal bills and deny a $200 billion hike in the debt ceiling.
Veteran Liberal MP Bronwyn Bishop was elected Speaker on Tuesday on the first day of the 44th parliament, which began with an indigenous welcome to country and traditional pomp and ceremony.
But the real business of parliament starts in earnest on Wednesday, with the introduction of coalition government legislation and the first parliamentary question time in more than four months.
The prime minister will personally introduce bills to abolish the carbon tax from July 1 next year and unwind Labor's climate change agencies and funding bodies as promised ahead of the election.
"This is an absolutely vital piece of legislation," Mr Abbott told reporters in Canberra.
Opposition Leader Bill Shorten says Labor will support the carbon tax repeal, but only if the government bows to its demand to introduce an emissions trading scheme in 2014.
Business groups argue fear delays to the repeal will cost jobs and dent investment confidence.
"I trust 'electricity' Bill Shorten will have a light bulb moment and will appreciate the people's verdict must be respected," Mr Abbott said.
The government will put up four other bills on Wednesday, including Treasurer Joe Hockey's proposal to raise the national debt ceiling from $300 billion to $500 billion.
But Labor is expected to secure Australian Greens support in the Senate to for a lower $400 billion ceiling, putting pressure on the government to accept an amendment given the current ceiling will be reached on December 12.
"What they didn't win in the election is the right to run up debt like a drunken sailor and to simply say trust us and we'll be back later to tell you what's going on," Mr Shorten said.
"We've offered a sensible compromise."
Earlier, lower house members and six senators took their oaths and affirmations, just after Chief Justice Robert French declared parliament open with the authority of the Governor-General.
Ms Bishop was elected the 29th Speaker of the House of Representatives, defeating Labor nominee Rob Mitchell.
"She is a formidable character," Mr Abbott said.
Ms Bishop, who wants to be addressed as Madam Speaker, said she would act impartially and ensure parliament was a "strong and robust place of debate".
"There will be times when there will be turbulence ... when we can feel the heat and anger of the place rises, but it will be my job to try and keep that order while remaining a place of robust discussion of ideas."
Formally addressing both houses, Governor-General Quentin Bryce said Australia had voted for change and the government had a clear plan for a strong, prosperous economy.
She singled out the National Disability Insurance Scheme as a "vast undertaking almost without precedent in our national life".
The government is also expected on Wednesday to introduce laws to repeal the mining tax, bring back the Australian Building and Construction Commission and enforce tougher penalties for union corruption.
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