Crossbench MP Rebekha Sharkie says her support for the Turnbull government is on a "day-by-day" basis.
The government, which was left with a one-seat majority after the 2016 election, is down one MP as John Alexander fights a by-election in his NSW seat of Bennelong.
This makes it all the more critical Prime Minister Malcolm Turnbull has the support of the five crossbench MPs for confidence and supply.
Ms Sharkie, who represents the Nick Xenophon Team in the lower house, says she wants parliament to give its unanimous support to a referral of her dual citizenship case, as well as that of Labor and other coalition MPs, to the High Court.
"I take it day by day and I've given the government my confidence and I said I would support supply and I don't want to be seen as a wrecker," she told Sky News on Thursday.
"But I think the government is doing a very good job of wrecking the parliament themselves."
She says the citizenship issue can only be put to rest with a bipartisan approach.