There is a growing feeling among Coalition frontbenchers the Speaker's position is untenable, but little confidence that Bronwyn Bishop can be prevailed on to resign.

Mrs Bishop has been engulfed in a furore over her use of taxpayer-funded political entitlements, after it was revealed that she spent $5,227 on a charter helicopter to travel a short distance from Melbourne to Geelong for a political fundraiser.

Labor has also raised questions about expenses claims Mrs Bishop made to attend the weddings of two Liberal colleagues.

Her office says the travel has been taken within entitlements.

The ABC has spoken to senior members of the Government and there is little support for her. One described her position as "untenable", another called her actions "unconscionable".

All raised a large procedural hurdle: the Prime Minister cannot sack the Speaker, she can only be removed if a vote of no confidence is carried by the Lower House.

None believed the Speaker would fall on her sword but there is broad agreement among those the ABC spoke to that the continuing scandal surrounding Mrs Bishop is damaging the Government.

How can the Speaker be unseated? Speaker ceases to hold office if they cease to be a member.

Speaker ceases to hold office if they cease to be a member. Speaker can be removed from office by a vote of the house.

Speaker can be removed from office by a vote of the house. Speaker can resign their office or seat directly to the Governor-General in writing.

One said few in the party still backed the Speaker.

"Ropeable doesn't even come close," he said.

"This is week three and there is no sign of it ending. She has no support [in the party] because what she did was so unconscionable."

The minister said the story was dogging MPs and senators wherever they went.

"It's a disaster," he said.

Another frontbencher said: "No-one can sack her. She's got to resign and she's got nothing to lose. If she resigns that's the end of her career."

Another did not believe the Prime Minister would try to force the Speaker out: "She won't resign and he won't ask her to go."

One minister said he thought the furore was doing damage to the Government but that the Speaker should not resign.

Leader of the House backs Bishop to remain Speaker

The Leader of the House, Christopher Pyne, has called on Government colleagues to stand firm and support Mrs Bishop to remain in the Speaker's chair.

"Stand firm against the demands by the Labor party to remove the Speaker," he told Sky News.

"These issues do come and go, they're always extremely unhelpful, but you also don't jump at the first whiff of grapeshot."

Mr Pyne also praised Mrs Bishop's conduct.

"I think Bronwyn Bishop is doing a superb job as Speaker," he said.

Crossbench MPs Clive Palmer and Andrew Wilkie have confirmed they plan to lodge a "no confidence" motion in the Speaker when Parliament resumes.

Cabinet ministers unwilling to provide public support for Bishop

Communications Minister Malcolm Turnbull, a regular promoter of his use of public transport, took to Twitter to publicise his own trip through Geelong on Wednesday.

The tweets included a photo showing Mr Turnbull at South Geelong train station, on his way to Torquay.

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"At Sth Geelong station with @SHendersonMP before going to Torquay to inspect the @NBN_Australia rollout," he said.

In response to a question from a reporter about whether he had arrived in a helicopter he quipped: "There was no aerial component whatsoever."

Two other Cabinet ministers have publicly acknowledged that Mrs Bishop is considering her future.

"I understand that the Labor Party will seek to use this to destabilise Question Time for example, and I'm sure Speaker Bishop will take that into account as she considers her position," Foreign Minister Julie Bishop told Channel Nine.

Scott Morrison went a step further and said the Speaker was actively canvassing for support.

"The Speaker, I think, is consulting with her colleagues and I think that's the appropriate place for those discussions to take place," he told reporters in Queensland.

Opposition Leader Bill Shorten said Mr Abbott could no longer ignore the expenses "scandal".

"This is a test of Mr Abbott's leadership. He needs to act; this soap opera just needs to finish," Mr Shorten said.