Former Speaker Peter Slipper has already exercised his newfound power as an independent MP by voting with Labor to change standing orders against the wishes of the Coalition.

Opposition Leader Tony Abbott suggested yesterday Mr Slipper should always side with the Coalition and that he would be happy to accept his vote.

This was despite Mr Abbott insisting on Tuesday that Mr Slipper be sacked as Speaker.

Mr Slipper has moved to the crossbench after he resigned in disgrace on Tuesday night following heated parliamentary debate about offensive text messages he had sent to a former staffer.

He is defending a sexual harassment case in the Federal Court.

''How he votes is up to him,'' Mr Abbott said yesterday.

''But if he chooses to vote with the Coalition, we certainly will be happy to have that vote.

''Certainly, I would think that someone who was elected as a Coalition member would be inclined to support the Coalition's position.''

Mr Slipper quit the Coalition in November to become Speaker at the invitation of the government.

The Opposition Leader saw no contradiction yesterday in his willingness to accept Mr Slipper's vote while at the same time refusing what he describes as the ''tainted vote'' of former Labor MP Craig Thomson.

Mr Thomson moved to the cross- bench earlier this year amid claims he misused union funds for his own gain - claims he denies.

''Craig Thomson has been found by a quasi-judicial body to have misappropriated some $500,000 in low-paid union members' money,'' Mr Abbott said.

''So there is a fundamental difference between Mr Slipper and Mr Thomson.''

But while Parliament's newest independent MP sided with the government yesterday, he could be a problem for both sides of the House if he flexes his muscle and demands he be courted for his vote each time.

Mr Slipper, who loses a number of parliamentary entitlements and significant salary, now sits on the crossbench with fellow independents who forced his resignation.

Independents Rob Oakeshott and Tony Windsor revealed yesterday that they met with Mr Slipper on Tuesday, telling him they would vote with the opposition to sack him unless he volunteered to resign.

The pair said they had convinced Mr Slipper that his position as Speaker had become untenable and that he should salvage whatever scrap of dignity he could by quitting.

Both MPs voted with the government against Mr Abbott's motion to sack Mr Slipper because they had secured Mr Slipper's guarantee he would resign.

Meanwhile, Prime Minister Julia Gillard's refusal to sack Mr Slipper once the text messages had been revealed has brought her judgment into question.

Deputy Opposition Leader Julie Bishop described Mr Slipper's willingness to resign as a ''grubby political deal'' and said Ms Gillard should have acted decisively because the text messages were offensive to women.

''Instead of being remembered as Australia's first female Prime Minister, she'll be remembered as the Prime Minister who let down the women of Australia when she was put to the test,'' Ms Bishop said.

However, Ms Gillard's parliamentary attack on Tuesday against what she described as Mr Abbott's misogynistic and sexist behaviour went viral yesterday and was applauded by women across the world.

She repeated some of those sentiments yesterday.

''Enough is enough. I've had enough. Australian women have had enough,'' Ms Gillard said.

''When I see sexism and misogyny I'm going to call them for what they are.''

Mr Abbott accused Ms Gillard of using the gender card and said her attack was ''a bit rich''.

''Just because the Prime Minister has sometimes been the victim of unfair criticism doesn't mean she can dismiss any criticism as sexism,'' he said.

Slipper Takes His Revenge On Opposition