Arguably, though they are far less spectacular, Bronwyn Bishop’s claims for trips during which she attended the weddings of Liberal colleagues in 2006 and 2007 are even more red-hot than the notorious helicopter ride.

But, as of Wednesday, neither claim – which Bishop justifies on the basis that she also had confidential meetings with people in relation to her work as chair of a parliamentary committee – was included in the scrutiny being undertaken by the Finance Department.

The only matter so far referred to Finance – by the Australian Federal Police after a letter from Labor – was the infamous flight between Melbourne and Geelong.

Yet the government is giving the impression that the suite of controversial Bishop claims is currently under examination.

Foreign Minister Julie Bishop said on Wednesday: “I understand that the Department of Finance is carrying out an investigation into a number of the claims that have been made.”

Asked whether the Speaker should resign if she didn’t produce the paperwork showing that her travel was approved by the parliamentary committee, Julie Bishop said: “Well this is a matter for the Department of Finance … I’m not going to pre-empt the Department of Finance’s enquiries or findings.”

If the wedding trips are to be put under the microscope, either there needs to be a fresh complaint or Finance has to take them up itself.

While the helicopter journey mightn’t pass the “sniff test”, Bishop could and did insist the Liberal fundraiser she attended in Geelong was official business. Trying to justify the other claims on the grounds of secret meetings will be regarded by the public as decidedly whiffy without documentation.

The Bishop affair is now a full-blown crisis for Tony Abbott. Cabinet ministers are divided, sending out opposing signals.

Scott Morrison said on Wednesday that Bishop was “consulting with her colleagues”.

Julie Bishop, speaking from New York, said: “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.”

Julie Bishop is deputy leader of the Liberal Party. Her message seemed clear.

But Christopher Pyne, who is Leader of the House of Representatives, was off in another direction. “I’m certainly not going to jump on any bandwagon that’s trying to remove Bronwyn Bishop from the speakership. These issues do come and go, they’re always extremely unhelpful.

"But you also don’t jump at the first whiff of grapeshot and I’m standing strongly behind Bronwyn Bishop as the Speaker and I would call on all my colleagues whether they’re in the cabinet or on the backbench to stand firm against the demands by the Labor Party to remove the Speaker.”

It’s unlikely Pyne’s characterisation of this as one of those “unhelpful” issues that “come and go” will fit well with the public mood.

Pyne also said Bishop was doing a “superb job” as Speaker and he did not believe she was “going anywhere”.

If Bishop is thinking about her position, she is certainly not giving any public sign of it. Her spokesman said that “the Speaker is not resigning”.

Crossbenchers Clive Palmer and Andrew Wilkie have announced they will move a motion of no confidence in Bishop when parliament resumes the week after next unless she quits the speakership.

Wilkie said Bishop “has abused parliamentary entitlements and treats public expectations with contempt. No wonder many members of the community question her integrity.”

Apart from the entitlement issue, Palmer and Wilkie also pointed to Bishop’s bias in the chair.

If Bishop is still in her job, how will Abbott defend her in the no-confidence motion? Whatever he says, the take-out by voters will be that he is condoning the rorting of entitlements. Or would he leave the defence to Pyne?

As he contemplates how much damage the furore around Bishop, his ally of many years, could do, Abbott has only to look at this week’s Essential poll. Fewer than one in five (19%) believed Bishop should remain in the position of Speaker; 25% said she should stand down while an investigation was done; 19% wanted her to resign as Speaker and 24% said she should resign from parliament.

The coming parliamentary session will be difficult enough for Abbott. The weekend Labor national conference has helped Bill Shorten, who will go into the next session stronger than he left the last one. The same-sex marriage issue is messy for Abbott. If he has to face a prolonged pitched battle over Bishop, Abbott could soon find his authority, always fragile, once more eroded.

With a number of senior colleagues judging Bishop’s position as untenable or a serious drag on the government, they could become increasingly critical of Abbott if he stands by her and the affair is seen to take a toll on the Coalition’s standing.

Malcolm Turnbull, who these days plays the role of cabinet’s free spirit, delivered a devastating critique of Bishop and a message to Abbott on Wednesday, when he travelled by tram and train from Melbourne to Geelong. The trip – a fraction longer than an hour by train – was relayed by tweets and photograph.

The best course for Abbott would be to persuade Bishop to leave her post (he couldn’t remove her against her will except by a vote of the House) so that, on the day parliament resumes, the government could propose a new Speaker to the House.

It’s yet to be seen, however, whether Abbott wants Bishop out, or could get her to quit.

Clarification: When the AFP referred the helicopter flight to Finance, Bishop also asked for two charter flights – not connected with the weddings – to be included in the review.

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