The federal government was rocked by revelations that Deputy Prime Minister Barnaby Joyce, deputy Nationals leader Fiona Nash and former cabinet minister Matt Canavan are dual citizens, which puts them in breach of section 44 of the constitution, and endured a torrid week in Parliament last week.

At the same time, public debate in the Coalition over protections for religious freedoms, if same-sex marriage is legalised, have escalated and caused another distraction for the government.

Fairfax Media spoke to half a dozen MPs in the Liberal Party on Monday who blamed the citizenship debate, and to a lesser extent the same-sex marriage postal survey, for the Coalition's fall to a 46-54 per cent two-party-preferred share in Newspoll, as well as hits to Mr Turnbull's preferred prime minister and satisfactions ratings.

When Mr Turnbull took the leadership in 2015, he cited the Coalition trailing in 30 consecutive Newspolls as one of the reasons for his move. The Coalition has now trailed in 18 consecutive Newspolls.

Veteran Queensland MP Warren Entsch said the citizenship revelations had been a fiasco and that "it creates the perception that we are focused on this, rather than dealing with the issues, and that hurts us".

"People think it [the citizenship issue] is bullshit, but we are the government, and this has played a role in the Newspoll [result]. The solution is to get this dealt with - hopefully the High Court will resolve this quickly and sensibly."

And NSW MP Craig Kelly said a full audit should be conducted - after the High Court rules on Mr Joyce, Senator Canavan and One Nation senator Malcolm Roberts. Both major parties have so far resisted calls for an audit, which the Greens have also backed.

The High Court will hold a preliminary directions hearing on this case on Thursday, but the matter is not expected to be dealt with until October.

Asked if the citizenship issue had hurt the government, Mr Kelly said: "It is very damaging – people see there is chaos...and the government is the one who wears it, irrespective of whether or not it is something completely outside the government's control."

"It has been a frustrating issue [citizenship], that has taken away from a lot of the work the Coalition government is trying to do, to act on things that we need to do – the action we are taking on electricity prices and the action we are taking to try and get the budget back in balance, the actions we are taking on national security."

A third MP, who asked not to be named, said voters believed the looming postal survey on same-sex marriage and the citizenship issue were government navel-gazing while a fourth MP said he had expected the poll result to be worse, given what had taken place last week.

Mr Entsch also suggested that Labor needed to be "very careful about jumping up and down about this" as it may well turn out it also has MPs who have broken the rules.

The government has attempted to turn up pressure on Opposition Leader Bill Shorten, demanding he release papers proving he has renounced British citizenship, while also questioning whether other Labor MPs including Susan Lamb, Justine Keay, Tony Zappia and Maria Vamvakinou were eligible for election - even though those MPs have released detailed breakdowns of what steps they took to ensure they were not dual nationals.

Mr Shorten said on Monday he would not be distracted by the polls but "the Turnbull government is totally obsessed with Newspoll".

He repeated previous public statements that he had renounced his British citizenship in 2006 and mocked the government's "newest conspiracy that I am a secret English agent. The reality is that no, I am not."

"We [Labor] have a strict vetting process. There is no cloud over any of our people, let's be straight here...it is not Labor's fault if government MPs and senior government ministers are not in compliance with the constitution."

On Monday, Turnbull government frontbenchers also publicly disagreed over whether legalising same-sex marriage had implications for religious freedom.

Attorney-General George Brandis insisted that religious freedoms would still be protected and suggested the postal survey and that the postal survey was about the rights of two people of the same gender.

But junior frontbenchers Angus Taylor and Zed Seselja disagreed, arguing it would affect religious freedom, parental rights and freedom of speech.

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