After months of scandals, Gillard acted to clear the political air on Sunday by sidelining two lawmakers facing unsavoury allegations which she said had resulted in a line being crossed about respect for parliament.
But she remains under intense pressure to call an election, not due until 2013, with a poll in Sydney's Daily Telegraph revealing 52 percent of voters were in favour of a vote of no confidence in her government.
"We've got a lot of work to do and we know that," Finance Minister Penny Wong told Channel Nine in response to the poll of 1,019 people which showed Labor's vote had dropped to just 30 percent -- from 34 percent in January.
But she said Gillard had "made the right call in what has been a pretty difficult circumstance" in relation to the scandals involving parliamentary speaker Peter Slipper and ex-Labor lawmaker Craig Thomson.
Slipper is accused of sexually harassing a staffer and misusing travel entitlements and Thomson of using the credit card of his former employer, a trade union, to pay for prostitutes, lavish meals and to get cash advances.
Both men strongly deny the claims but Gillard said Slipper had agreed to stand aside as speaker indefinitely, while Thomson has quit the Labor Party and will move to the crossbenches until his matter is resolved.
The scandals have increased speculation that Gillard, who scraped into power after 2010 elections resulted in a deadlocked parliament by forming a coalition with a Greens MP and several independents, may face a new leadership challenge.
The loss of Thomson reduces Labor's numbers in the 150-seat House of Representatives and she must rely on the support of a Greens MP and two independents to have control of 74 votes. The opposition controls 73 votes.
Gillard saw off a leadership ballot against former prime minister Kevin Rudd in February, crushing him 71 to 31 in a Labor Party room vote, but speculation is mounting that her time is running out.
Trade Minister Craig Emerson said he had not spoken to Labor colleagues about dumping Gillard, but said there was "always chatter about this sort of thing".
But he added: "Her job is safe because she is a leader with gutsy determination."