Trade Minister Simon Birmingham says not supporting the coalition's full $158 billion tax cuts package would be "a stain that will haunt Labor and Anthony Albanese all the way to the next election".
But some advocates are calling for all sides of politics to put the brakes on putting the costly tax cuts into law, and instead dissecting them through a Senate inquiry.
The coalition needs the support of Labor or four of six crossbenchers to get its full three-stage plan through the Senate when parliament resumes this week.
So far the opposition has refused to back the full plan, offering to support extra tax relief only if the second stage of the package is brought forward and the third stage is shelved.
The coalition is flatly refusing to split the bill.
Labor frontbencher Katy Gallagher said the party will consider its position on the package when its caucus meets early this week.
But what they decide may not be the party's final stance, as they keep an eye on whether the government gets enough crossbench support.
"We would have to take decisions based on what was happening at the time," Senator Gallagher told Sky News on Sunday.
Senator Birmingham said Labor is ignoring the mandate Australians gave it at the election to deliver tax relief.
"Our policies were clear at the election and they were endorsed at the election," he told reporters in Adelaide.
"The failure to deliver tax relief for hard-working Australians will be a stain that will haunt Labor and Anthony Albanese all the way to the next election if they block this agenda."
The first stage of the plan will provide up to $1080 extra for low and middle-income earners when they lodge their tax returns in the coming months, as an offset for them is doubled.
Labor wants the second stage, which is due to kick in from 2022/23, to be brought forward to the coming financial year.
That stage will top-up a low income tax offset and mean more people will get a 19 per cent tax rate.
The final stage will flatten the tax rate from 32.5 per cent to 30 per cent for people earning between $45,000 and $200,000 from mid-2024.
Among Labor's concerns about the third stage are that it will be locked in too far in advance and there may not be enough money in the budget to pay for it.
Left-leaning think tank the Australia Institute shares those concerns, and is calling for the laws to be examined by a Senate inquiry.
Executive director Ben Oquist said there's an argument for passing the first two stages of the tax cuts quickly to stimulate the economy.
But there's no such impetus for the third stage.
"Never before has so much budget outlay been proposed without a serious Senate inquiry," he told reporters of the package in Canberra.
"The tax cuts that don't come in until 2024 don't need to be rushed through parliament this week."
Labor is also concerned too much of the benefit of the third stage of tax cuts may flow to people earning more than $180,000 each year, who are less likely to spend the cash and stimulate the economy.
Modelling released on Friday by the Parliamentary Budget Office showed 31 per cent of that will flow to people earning more than that figure, which will make up only 11 per cent of taxpayers in a decade.
Australian Associated Press