The Turnbull government will use Labor senator Katy Gallagher as a guinea pig case in the High Court to smoke out three of her lower house colleagues with similar citizenship doubts.
Leader of the House Christopher Pyne said the government is unlikely to refer any further MPs to the High Court this year unless it can win over an independent MP's support.
"If Katy Gallagher is disqualified, those three members should resign," Mr Pyne said, referring to Justine Keay, Josh Wilson and Susan Lamb, who also have UK citizenship doubts.
The High Court is due to go on a summer break from December 15 and is slated to return February 5.
Mr Pyne said it was a matter for the High Court to decide whether its comes back early.
Senator Gallagher will join Labor MP David Feeney at the court after the Victorian MP failed to find his UK citizenship renunciation paperwork from 2007.
The citizenship saga distracted MPs from the debate on same-sex marriage legislation on Wednesday, with the opposition seeking crossbench support for nine MPs to be checked for their eligibility.
Labor sought to end the fiasco, gaining the support of five crossbenchers to bring on a motion to refer four ALP members, four coalition MPs - Julia Banks, Jason Falinski, Alex Hawke, Nola Marino - and one independent Rebekha Sharkie to the court.
However, with the vote tied 73-all Speaker Tony Smith used his casting vote to defeat the motion.
The government is short one vote, with John Alexander facing a by-election in Bennelong in ten days.
Prime Minister Malcolm Turnbull said the motion "debased" the House.
Mr Shorten told parliament the Australian people wanted a bipartisan end to the saga.
"We need a circuit breaker to rebuild the confidence of the Australian people," he said.
Ms Sharkie said she accepted being on the list of those to be referred to the court.
"This cannot be a place for a protection racket of the highest order," she said.
Manager of Opposition Business Tony Burke had little sympathy for his colleague Mr Feeney, and stopped short of endorsing him to be Labor's candidate at a by-election for the marginal seat of Batman.
"When it came time to actually find the document, one of the documents hasn't turned up. Now, I find that weird," Mr Burke told ABC Radio.
Deputy Prime Minister Barnaby Joyce was on Wednesday re-sworn in to parliament after winning the by-election in the seat of New England after the High Court disqualified him for having New Zealand citizenship.
He has reiterated his call for a referendum on section 44 of the constitution.
But Pyne dismissed the idea, pointing out the lack of success of past referendums.
"I think we need to work within the rules the High Court has created," he said.