Australian Greens MP Adam Bandt and independent MP Andrew Wilkie expressed frustration that the fight between the two major parties was taking up time when parliament could be passing marriage equality law.
Labor is attempting to refer nine federal MPs to the High Court over doubts about their citizenship status.
A vote to refer eight other MPs to the court was narrowly defeated in the House of Representatives.
Documents made public by Federal Parliament yesterday show former ACT chief minister Katy Gallagher, who gained British citizenship by descent through her father, submitted forms to relinquish her British citizenship on April 20 previous year.
Katter's Australia Party MP Bob Katter said that he had been talking to the public and they were sick of the fiasco.
She said she'd taken all reasonable steps to renounce her British citizenship.
Mr Feeney has been questioned over his links to Northern Island.
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That includes details dating back to their grandparents.
The citizenship disclosure regime has also uncovered several MPs who could have been disqualified in previous Parliaments, including WA senators Louise Pratt and Dean Smith, but the revelations have no bearing on their current eligibility.
On Wednesday, Labor tried to refer nine politicians - including Mr Feeney - to the court through a motion in the lower house, in a vote that was initially deadlocked at 73-all.
Senator Gallagher's declaration, lodged under new parliamentary rules for citizenship disclosure, also reveals she sat in the Senate as a dual citizen for nearly 18 months after filling a casual vacancy in 2015.
The government did not support referring its own members to the High Court, with the prime minister arguing that the paperwork published on the citizenship register showed that the government MPs did not have citizenship of the countries Labor had alleged.
Although Joyce easily regained his seat at a by-election on Saturday, the crisis still has the government precariously clinging to power and has already dented its ability to pursue its political agenda.