The Turnbull government appears to be one vote short of getting its personal income tax plan through the Senate without the need to change it.
Labor wants the package split, to provide relief for low and middle income earners from July 1, but not deliver the remainder, due to benefit those on higher incomes from 2022.
The Greens oppose the package outright.
However, maverick One Nation senator Brian Burston - who has fallen out with his leader Pauline Hanson and colleague Peter Georgiou - has signalled he is on board with the plan without amendment.
The two Centre Alliance senators, Rex Patrick and Stirling Griff, could also be on the government's side.
Senator Patrick told Sky News on Thursday his party had yet to come to a formal position, but he was inclined to split the bill and support the low-income tax cuts.
"We don't necessarily see a good reason at this point in time to legislate for tax cuts that occur in 2022 or 2023, so we would be happy to split the bill," he said.
"If forced to we would potentially support the entire cuts but obviously we want to wait and see what happens."
It is understood senators David Leyonhjelm, Cory Bernardi, Fraser Anning and Derryn Hinch are supportive of the package as it stands.
However, independent Tim Storer and senators Hanson and Georgiou want it split.
The crossbenchers' position leaves the coalition one vote short of passing the package.
"If the government wants to see those tax cuts implemented, they should split the bill," shadow treasurer Chris Bowen told reporters in Sydney on Thursday.
But Treasurer Scott Morrison is not backing down.
"We are prosecuting the case for personal tax relief for all Australians," Mr Morrison told ABC radio.
"We don't step back from our plan simply because the Labor Party don't agree with it."
The cuts from July 1 would see a low and middle-income tax cut offset introduced - worth up to $530 for individuals - and the 32.5 per cent threshold increased from $87,000 to $90,000.
Mr Bowen said his biggest concern is the tax cuts pencilled in for 2024.
Stage three of the plan would increase the top 45 per cent tax rate threshold from $180,000 to $200,000 while abolishing the 37 per cent tax rate, leaving all taxpayers earning between $41,000 and $200,000 on a rate of 32.5 per cent.
Independent Parliamentary Budget Office data released this week showed this final phase will be a $41.6 billion impost on the budget compared with an entire package worth $144 billion over the next decade.
However, Mr Morrison disputed the accuracy of the year-by-year costings.