Federal Opposition Leader Tony Abbott has called on key independent MPs Tony Windsor and Rob Oakeshott to withdraw their support for the government.
Mr Abbott says there is no point in the coalition tabling a no-confidence motion to remove the government until the pair pull their support.
"The two people who are propping up this government, the two people on whom Julia Gillard utterly depends, are Mr Windsor and Mr Oakeshott," Mr Abbott told the Seven Network on Monday.
"There won't be a no-confidence motion until those two gentlemen wake up to themselves and listen to their electorates."
Mr Abbott said Labor's ditching of embattled MP Craig Thomson on Sunday was all about saving Ms Gillard's job.
Mr Thomson's membership of the ALP has been suspended but he will stay in parliament and continue to support the government from the cross-bench.
Peter Slipper has also been sidelined from the Speaker's chair as investigations into his alleged misuse of Cabcharge taxi dockets continue.
But Mr Abbott says Ms Gillard can't simply disown Mr Thomson, who's under investigation over alleged misconduct during his time as head of the Health Services Union (HSU).
"The prime minister can't disown Mr Thomson's membership of the caucus without disowning his vote as well," Mr Abbott added.
Meanwhile, former ALP leader Mark Latham says the Gillard government is on the brink of collapse.
"Well, she's in a terrible situation," he told Macquarie Radio Network.
"No one buys this `line in the sand' approach.
"This is just a convenience to try and clear the decks politically for the federal budget next week."