Labor has recruited former NSW premier Kristina Keneally to run in the Bennelong by-election, in a surprise move which could destabilise the Turnbull government.
The announcement by Labor leader Bill Shorten came as the citizenship crisis - which triggered the December 16 by-election - claimed the scalp of maverick Tasmanian senator Jacqui Lambie.
Senator Lambie, the daughter of a Scottish-born father, on Tuesday revealed in a tearful speech to parliament UK authorities had confirmed her status as a British citizen by descent - which compelled her to resign.
She warned the government against using her absence as an opportunity to pass legislation she opposed, such as workplace reforms, but backed yet-to-be-passed laws for a first home buyers superannuation scheme.
Liberal MP John Alexander's dual citizenship triggered the by-election in his Sydney seat of Bennelong.
Mr Shorten said the by-election was the chance to send a wake-up call to the Turnbull government.
"This is a chance which I think a lot of people in Australia would like to have that has fallen to the people of Bennelong to send a message against the dysfunction and the chaos of the current government, the policy paralysis, the failure of leadership," he told reporters in the electorate.
Prime Minister Malcolm Turnbull told reporters in Manila, where he is attending the East Asia Summit, the voters of Bennelong already had an "outstanding representative" in Mr Alexander.
"My message to the voters of Bennelong is ... don't let Kristina Keneally do to Bennelong what she did to New South Wales," he said.
Las Vegas-born Ms Keneally has released documents showing she renounced her US citizenship in 2002.
"Who could have imagined that this citizenship crisis would end up with people like John Alexander sitting there quietly for months, not revealing that he may well be a dual citizen?" she said.
Cabinet minister Greg Hunt fired the first shot from the coalition trenches, describing Ms Keneally as "Eddie Obeid's protege" - referring to the disgraced former state Labor minister.
Attorney-General George Brandis told parliament there was "incontrovertible evidence" two Labor MPs - Susan Lamb and Justine Keay - had not completed renunciation of their UK citizenship at the time of the 2016 election.
He denied suggestions the government was in chaos.
"There is no constitutional crisis, there is no political crisis," he said.
"There is the unexpected effect of a decision of the High Court which has resulted in both houses of the parliament now having had members resign or be referred to the Court of Disputed Returns."
Senator Lambie has expressed an interest in running for Ms Keay's northern Tasmanian seat of Braddon should the Labor MP face a by-election.
Mr Turnbull confirmed on Tuesday he would await the result of a process for all members of parliament to disclose their citizenship and family history details before endorsing any further referrals to the High Court.
That would leave any lower house MP referrals until at least December 4, the next sitting after the December 1 deadline for the information to be lodged.
Senator Brandis said a referendum to change the constitution, while not government policy, should be "at least canvassed" in a parliamentary inquiry.
There was also the possibility of changing Australia's citizenship laws to allow the renunciation of "unwanted foreign citizenship".
