The Labor-led government appears to enjoy the 'confidence' of key Parliament members following the temporary exit of House Speaker Peter Slipper on Sunday amidst accusations of corruption and sexual misconduct.

Slipper has decided to step aside after a former media aide, James Ashby, filed sexual harassment charges against him plus allegations that he misused his Parliamentary entitlements by paying for expensive limousine services this year in Sydney.

The surprising developments floated the likelihood that Prime Minister Julia Gillard's government would be replaced much sooner as the Coalition urged members of the Parliament to support a no-confidence initiative against the ruling Labor Party, specifically enjoining independent lawmakers to muster the 76 votes needed to oust Ms Gillard.

Members of the opposition faulted Ms Gillard for entrusting the House Speakership post to Slipper, who last year bolted the Liberal Party and turned independent to assume 'leadership' of the House of Representatives.

However, Independent MPs Tony Windsor and Rob Oakeshott have declared on Monday that they will keep supporting Ms Gillard despite the latter admitting that Slipper's current predicament brought an overcast of 'darkness' over the minority government, already battling prospects of electoral defeat next year.

Windsor, on his part, has indicated that his support for the Gillard government was not in any way affected by the Slipper controversy.

He, however, qualified that his present position could change "if there's corrupt activity (within government) or maladministration," as reported on Tuesday by The Associated Press (AP).

Also, the Australian Green Party, which supports the Labor government, issued assurances that Ms Gillard still has the party's backing and assailed the opposition at the same time for trying to convert the Parliament into a court to grab control of the federal government.

Opposition Leader Tony Abbott has ramped up his criticism of Ms Gillard for engineering the ascension of Slipper last year to the House Speakership despite what he claimed as Slipper's shaky reputation during his tenure as Deputy Speaker in the Liberal government of John Howard.

"Certainly there have been various Department of Finance investigations into Mr Slipper in the current parliament, including when he was deputy speaker in 2011," Abbott told the Australian Associated Press (AAP) on Tuesday.

He added that Ms Gillard was well aware of the questionable acts that had hounded Slipper even prior to the Labor government's support for his ascension to the House Speakership in November last year, which provided a much-needed boost to Ms Gillard's minority rule.

The Prime Minister, however, dismissed suggestions that she knew so much of Slipper when the latter was tapped as the new House Speaker, who the Labor government can rely on.

Speaking to reporters in Singapore on Monday, Ms Gillard insisted "I don't claim to know Mr. Slipper personally or well, but I formed a professional judgment about his ability to do the job."

But Abbott scored Ms Gillard for attempting to downplay the seriousness of the accusations being hurled against a key leader of the Parliament.

"She just doesn't get it when it comes to the seriousness of this and the appalling cloud which now hangs over not just the Parliament but her and her government," Abbott told The Sydney Morning Herald on Tuesday.

Yet according to Attorney-General Nicola Roxon, the opposition leader was obviously overreacting and his excitement was acting "like the leader of a lynch mob," raring to pounce on the opportunity presented by Slipper's quandary.