Two senators gone in less than a week
Now, the failure to vet candidates properly has left the Greens without a quarter of their voting bloc in the Senate.
But Prime Minister Malcolm Turnbull is not sympathetic, telling Channel 9 the Greens have simply been sloppy.
"It is pretty amazing, isn't it, that you've had two out of nine Greens senators who didn't realise that they were citizens of another country. And it shows incredible sloppiness on their part. You know, when you nominate for parliament, there is actually a question. You've got to address that Section 44 question, you've got to tick the box and confirm that you're not a citizen of another country. So, it is ... it's extraordinary negligence on their part."
Under Section 44 of the constitution, dual citizens are not eligible to be elected to parliament.
The same rule does not apply in countries like Britain and Canada.
British foreign secretary Boris Johnson renounced his United States citizenship last year, but only because he had to pay taxes there despite leaving as a five-year-old.
Opposition Leader Bill Shorten says his party does a proper vetting of each of its candidates before they can run for their seat.
"When you're a Labor candidate, you're required to confirm your citizenship and (that) you're not a citizen from another country. And we don't just rely on someone ticking a box. I understand, from speaking to the party administration, that, if you're born overseas, you have to record that fact and tell the party. If you've got a parent who's born overseas, then you have to show what steps you've taken."
For Labor senator Sam Dastyari, for example, renouncing his Iranian citizenship was no easy feat.
He says he spent $25,000 on legal fees.
"I believe I've taken the most extraordinary steps of any Australian parliamentarian ever to meet their Section 44 requirements. And I have to say, I believe it's unfortunate that Scott Ludlam and Larissa Waters didn't take what were simple steps to them to meet their requirements. I don't have any doubt that they love Australia, that they're loyal to Australia and that they're passionate about being an Australian, but the rules are the rules, and, while we can have a debate about whether this part of the constitution should exist or should be reformed, it's there, and all parliamentarians knew it was there before they ran for parliament."
Larissa Waters and Scott Ludlam, the two Greens senators who have resigned, could be forced to pay back more than a million dollars each in wages earned in their Senate careers.
But Greens leader Richard Di Natale has told the ABC that would be unfair.
"They shouldn't be. They've done their job. They've represented their states. They've continued to legislate in parliament. They've attended, I'd have to say, more diligently and more often than most other senators. Effectively, every Greens senator is a shadow minister, because we hold portfolios, where they're travelling the country. Larissa's a young mother -- she's made huge sacrifices there."
With a quarter of Australia's population now born overseas, a question has been raised about whether the constitutional provision is archaic and even discourages diversity.
But changing Australia's constitution would require a referendum, and history shows referendums often fail.