Victorian independent MP Cathy McGowan has run out of sympathy for the dual citizens in her midst.

In a pivotal balance-of-power position in the house of representatives, McGowan believes it’s time not only for a full audit of all MPs and senators’ citizenship status but for criminal penalties to be imposed for inaccurately filling out their nomination forms in the first place.

The revelation that senate president Stephen Parry is not only a British dual citizen but that he waited until after the High Court’s recent ruling to come forward – apparently hoping he wouldn’t need to – has prompted McGowan and her crossbench colleagues to demand that all MPs clarify their status.

They also want the enforcement of criminal penalties for false statements, a threat they argue would make candidates and parties undertake more comprehensive checking.

McGowan has told The Saturday Paper that expulsion from parliament should not be the only penalty for transgression of section 44(i) of the Australian constitution.

“I’m really at the stat dec stage,” McGowan says. “A stat dec is a legal document that people sign regularly and I think that’s really where we need to do the work.”

“It’s a legal issue. We should treat it like we do with people who commit fraud on social security. That’s where I’d like the investigation to go.”

When nominating for election, candidates sign a declaration that they are eligible on the grounds set out in section 44. But once elected, any parliamentarian who discovers they may hold other citizenships can quietly renounce them. If they can make it to the next election with nobody finding out, there is no retrospective penalty for being in parliament unlawfully.

McGowan wants false electoral nomination declarations to be treated the same as false declarations on any other government form: deemed to be a breach of the Crimes Act and attracting

a potential penalty of four years’ jail.

She believes the government’s referral of the High Court’s decision in the cases of former deputy prime minister Barnaby Joyce and six – soon to be seven – senators to the joint standing committee on electoral matters should also cover the enforcement of penalties.

“I actually see this as a really important issue,” McGowan says. “It’s a legal issue. We should treat it like we do with people who commit fraud on social security. That’s where I’d like the investigation to go.”

She is not ruling out withholding support for government legislation to secure agreement, but says she is not threatening that “at this stage”.

McGowan is backing Greens leader Senator Richard Di Natale’s proposal that an independent body conduct an audit and then refer doubtful cases to the High Court.

“There are a range of ways you could do it,” Di Natale told the ABC’s 7.30 program on Tuesday, after Parry’s revelation.

“You could do it through the independent parliamentary expenses authority and empower them to conduct it. You’d only need a small number of immigration lawyers. A senior bureaucrat could knock it over inside a month. Then we’d know very clearly who’s ineligible to stand and deal with it all at once, rather than this drip-feeding that’s going on at the moment that really is distracting everybody.”

The government has dismissed the audit idea out of hand.

Treasurer Scott Morrison ridiculed it as being like “some reality television show of Who Do You Think You Are?”.

“Australians are more interested in their jobs than people’s genealogies,” Morrison said on Thursday.

“The idea that somehow we need to set up the office of the public genealogist I think is getting a bit ridiculous.”

McGowan and the Greens are not alone in believing an audit and stronger enforcement are required.

Independent Andrew Wilkie also supports a wholesale examination of parliamentarians’ citizenship. He says there’s “almost a ceasefire of sorts declared” between the major parties.

“I think it’s in both their self-interests not to have an audit, but of course, it’s not in the public interest,” Wilkie told ABC Radio National.

Fellow crossbench MP Bob Katter says he had previously queried calls for an audit because of the risk of innocent people being caught up in a witch-hunt. But he thinks the deteriorating situation makes it necessary.

“I’ve changed my position, to be honest,” Katter says. “I’ve been thinking about this. It’s just not good enough.”

He also supports enforcing penalties for inaccurate declarations.

“I think there should be some form of retribution here. I mean, after all, you have filled out a form.”

He says McGowan’s idea should be “seriously considered”.

“I’m with Cathy on this,” Katter says. “We should find them and boot them out.”

MP Rebekha Sharkie, from the Nick Xenophon Team, supports both an audit and an examination of tougher penalties for false declarations.

“I think that’s fair,” Sharkie told The Saturday Paper.

“Obviously it’s about whether you knew at the time you were giving a false declaration. But I think we need to do all we can to get back some of the faith from the community.”

Sharkie cites major-party obstruction in the past, over entitlements.

“We tried to get up greater penalties when people do the wrong thing around travel, and both the major parties wouldn’t support it.”

Ex-Liberal crossbench senator Cory Bernardi, who formed the Australian Conservatives, wants parliamentarians to be made to sign new declarations in the wake of the court ruling.

“Get them to sign a statutory declaration and then if they’re found to have falsified that stat dec they actually face a term of imprisonment or a significant fine,” Bernardi told Sky News.

“Put the weights on them because I reckon there’s more, still more.”

Others share his view.

Right across the political spectrum, members, senators and their staff are saying privately they suspect there are more. But in the absence of further confessions, it is being left to the media to pursue constitutional compliance.

Journalists – with private encouragement from various parties’ spear-carriers – are compiling lists and chasing down the status of more than 20 other MPs and senators across the parties who have not produced evidence to support their dual-citizenship denials.

Those in the doubtful column include more than a dozen from Labor and at least another half-dozen Liberals.

Logic suggests that given five senators have turned out to have been ineligible among an upper house numbering 76, it is likely more than one of the 150 members of the house of representatives may also have a problem.

The Labor and Liberal parties are relying on the doctrine of mutually assured destruction and the biblical principle of letting those without sin cast the first stone.

The major parties are declining to level accusations at any of each other’s members whose heritage might jeopardise their eligibility. Once that first rock is hurled, nobody knows the damage that might be wrought.

Both parties had claimed their superior vetting procedures meant none of their members were at risk.

But the admission from Stephen Parry – who as senate president signed six of the citizenship referrals to the High Court – is threatening to shatter that détente.

Attorney-General George Brandis is hoping it will hold.

“If anybody wants to make an allegation that a member of parliament was not duly elected because of a section 44 issue, or for any other reason for that matter, then let them make that allegation,” Brandis said on Tuesday, after Parry’s revelation.

He later told ABC Radio National: “I don’t favour having some kind of witch-hunt.”

Neither does the opposition.

Asked about an audit, acting leader Tanya Plibersek said: “We’re very confident that no Labor MP is a dual citizen.”

All Labor MPs and senators are being encouraged to use the qualifier about being “confident”, avoiding an absolute declaration.

“We’ve got very strict processes, we’ve got very careful procedures when people are applying to be candidates,” Plibersek insisted.

She said all the “chaos” was with the government.

“They’ve got Liberal and National MPs who plainly were elected when they were not eligible to stand. It’s been dragged out of them kicking and screaming… I would’ve thought every single member of parliament and every single senator would’ve been double-checking their own eligibility if they had any doubts at all.”

But with Labor staking everything on their members not being affected, there are murmurs that some are being told it is better not to check.

The government is emphasising individual responsibility.

“It’s incumbent on every individual member and senator in the Australian parliament to comply with the constitution,” Finance Minister Mathias Cormann told the ABC’s 7.30.

“…And if we become aware of information that we might be in breach, we need to take the appropriate steps.”

He says the burden of proof is on those alleging a breach.

Cormann argues an audit would not resolve the issue because, under the constitution, only the High Court can determine eligibility.

But the proposed audit doesn’t seek to usurp the High Court. It would form a threshold test to identify those who are only Australian citizens, those – such as former senator Parry – who clearly hold dual citizenship and those whose status is unclear.

Those latter cases would then be referred to the High Court.

Some argue it amounts to a reverse onus of proof and would also be unfair to those whose heritage automatically bestows citizenship of countries that do not allow renunciation, potentially leaving their status under a cloud and jeopardising their ability to contest future elections.

Others counter that the constitution allows for those who have taken “all reasonable steps”.

Subjecting the whole parliament to a citizenship audit that unearthed more lower-house dual nationals could see the Coalition lose government. Alternatively, it could see Labor’s numbers drop, making the government more secure.

There would need to be more byelections or possibly an early federal election.

Neither major party wants to explore those scenarios.

The former chief of staff to then prime minister Tony Abbott, Peta Credlin, has accused the parties of colluding, saying she believes “there has been conversations had via whips, via leaders, via people on the inside that this is going to end in tears if this is pursued”.

No evidence of that has been produced.

But on Sky News, Credlin revealed that when she was in Abbott’s prime ministerial office, there were deals struck with the opposition to stop attacking each other over issues of mutual disadvantage, such as parliamentary entitlements, “lest we have more casualties”.

That’s not to say they will eschew opportunities to score points against each other where possible.

Labor hopes to use the government’s slimmer grip on power – in the absence of Barnaby Joyce, now facing a December 2 byelection – during this year’s final two parliamentary sitting weeks to revive moves for a royal commission into the banks and to try to overturn government legislation cutting weekend penalty rates, which passed by a single vote.

Both would still require government MPs to vote with the opposition, something that’s unlikely, because losing even that kind of vote could have broader implications for the government.

The parliamentary guidebook, House of Representatives Practice, says: “A vote by the House agreeing to a particular legislative measure or provision contrary to the advice and consent of the Government could similarly be regarded as a matter of confidence.”

The government could then choose to resign or reassert its authority through putting its own confidence motion to a vote.

Cathy McGowan and Rebekha Sharkie continue to offer the Turnbull government support on both confidence and supply. But losing any vote would be embarrassing for Turnbull.

The audit question is now also becoming another weapon for conservative Liberals to whack the prime minister.

Those Liberal backbenchers advocating for an audit are all supporters of his predecessor Tony Abbott: Victorian former minister Kevin Andrews, Tasmanian former minister Senator Eric Abetz, and New South Wales Liberal MP Craig Kelly.

Some Nationals also favour an audit. NSW Nationals senator John “Wacka” Williams says he thinks it’s a good idea.

Williams is at the centre of the latest intra-Coalition brawl in the citizenship fallout, with the Nationals pushing for him to take the senate presidency now vacant through Stephen Parry’s resignation.

When the Coalition is in government, the presidency traditionally goes to the senior partner, the Liberals.

But with Liberal Hollie Hughes set to replace ousted Nationals senator Fiona Nash courtesy of having fielded a joint Coalition senate ticket in NSW at last year’s election, the Nationals are trying to lay claim to the presidency instead, arguing it was their party’s electoral success that secured government for the Coalition.

Prime Minister Malcolm Turnbull has given them short shrift.

As three Nationals ministers were among those whose citizenship woes went before the court – and two were thrown out of parliament – he is not feeling sympathetic.

Turnbull also encouraged MPs and senators to take responsibility.

“The obligation is a personal one on each member and senator,” Turnbull told journalists during his visit to Israel.

He also noted the significance of the candidates’ declaration.

“After all, when you run for parliament, you sign, you tick a box on the form which says you’re not in breach of section 44.”

Having not been told about Stephen Parry’s predicament until Tuesday – a full day after Parry told Attorney-General George Brandis – Turnbull also rebuked the suddenly retiring senator.

“I’m disappointed that Senator Parry didn’t make public this issue, some time ago, quite some time ago,” Turnbull said.

The Saturday Paper has been told Parry confided in at least one ministerial colleague that he feared he had a problem several months ago. Communications Minister Mitch Fifield has confirmed that he has known for weeks.

Parry did not return The Saturday Paper’s calls.

Labor’s senate leader Penny Wong said it was “more than disappointing that Senator Parry took so long”.

“The Liberal Party should have been checking this as the Labor Party has,” Wong said.

She echoed the finance minister’s arguments against an audit.

“Ultimately the only body under our constitution that can determine if an MP or a senator has dual citizenship and is not entitled to stand is the High Court. That is why we’ve had a process of self-referral.”

Former Keating government minister Graham Richardson, now a commentator on Sky News, summed up the cynicism of many watching the reignited citizenship debacle, taking a swipe at anyone who might be sitting quietly on the leather benches, worried they too might be unlawful but hoping to get away with it.

“Imagine sitting there, knowing you are a citizen of another country,” Richardson mused.

Yes, imagine. Who would possibly have an interest in doing that?