Centre Alliance MP Rebekha Sharkie supported the bill in the lower house, but said her two senate colleagues were still negotiating with the government on ways to reduce gas prices.
Centre Alliance senator Rex Patrick said the minor party was working through the finer details of a deal to make sure extra money in taxpayers' pockets doesn't get swallowed up by higher power bills.
Former Liberal Cory Bernardi also backs the tax relief package, leaving the government just one vote short.
Returning Tasmanian senator Jacqui Lambie is likely to be the deal maker or breaker, but she's yet to declare her hand.
Senator Lambie told reporters she hadn't come to a position yet, saying her staff only started work yesterday and she hadn't had enough information from the government.
WHAT DO THE TAX CUTS DELIVER?
The first stage of the plan will deliver up to $1080 to low and middle-income earners when they lodge their tax returns in coming months.
The second stage will top up a low-income tax offset, which means more people - earning up to $45,000 instead of $41,000 - will get a 19 per cent tax rate.
The final stage flattens the tax rate from 32.5 per cent to 30 per cent for people earning between $45,000 and $200,000 from mid-2024.