Labor has lost its majority party status in parliament's lower house amid increased speculation about Prime Minister Julia Gillard's leadership.
The coalition now has 72 seats - one more than Labor - in the House of Representatives following a decision by West Australian Nationals MP Tony Crook to quit the cross bench and join the opposition.
His move will have little or no effect on the floor of parliament but gives the opposition bragging rights for holding more seats than Labor.
The government will still need the support of at least four crossbenchers to have its legislative program clear the lower house.
The coalition, on the other hand, might need only two additional votes to stymie the government.
The change strengthens the hand of independent MPs opposed to flagged measures in Tuesday's budget, including an end to the diesel fuel rebate for miners.
Ms Gillard on Sunday sought to appease Labor MPs nervous about the impact a carbon tax is likely have on household budgets from July 1 by announcing a school kids bonus.
About 1.3 million eligible families - those entitled to Family Tax Benefit A - will receive $410 for each child in primary school and $820 for each child in high school.
A typical family will receive about $700 more than it was entitled to under the axed education tax refund scheme.
The government will rush legislation through parliament this week so a first payment can be made in mid-June.
The opposition says the bonus is a "sugar hit" designed to cushion the predicted impact of the carbon tax.
Labor MPs believe the carbon tax is killing the government in the electorate where support for the ALP is at near-record lows.
Speculation is rife that a significant number of Labor MPs, including some who backed Ms Gillard over Kevin Rudd in February's leadership showdown, are looking at dumping the prime minister and scaling back the $23-a-tonne carbon tax.
Finance Minister Penny Wong acknowledges the tax is a challenge for the government.
"There's no doubt it's a difficult policy but I think it's an important reform for the future," she said on Sunday.
High-profile trade unionist Paul Howes, who publicly disavowed Mr Rudd the night before the Labor caucus dumped him as prime minister in June 2010, says changing leaders again is not the answer.
"It looks messy, it looks bad," he wrote in the Sunday Telegraph, noting the Rudd dumping did not go down too well with voters.
"Australians don't like parties who dump leaders. They view that as their right."
Ms Gillard refused to buy into Mr Howe's reflections about the 2010 leadership change.
When asked whether it had been a mistake to change leaders, she told reporters in Canberra: "I've dealt with all of these questions a million times in the past. I'm not intending to today."
The Australian Greens, who back Labor in both houses of parliament, say they are prepared to renegotiate their post-2010 election agreement with a new prime minister if Ms Gillard is replaced.
But the minor party won't support changes to the carbon tax and other clean energy measures already passed by parliament.
"It has been something that was really hard fought," Greens leader Christine Milne said.