The federal government wants its income tax plan passed in one piece, but Labor will only back the first stage and crossbenchers also have concerns.
The Turnbull government's personal tax cut plan will almost certainly need to be split in order to clear parliament, with Labor and crossbenchers querying its cost.
Malcolm Turnbull insists the three stages of cuts, announced in Tuesday's federal budget, are part of a whole plan and must be passed in their entirety.
"What we're saying is that hardworking Australian families, particularly middle-income Australian families deserve to keep more of the money they earn - it is their money," the prime minister said on Thursday.
The bulk of Australians - 94 per cent - would not get "slugged" by going into a higher tax bracket if they won a promotion or worked overtime.
Labor is happy to support the first stage of the cuts in parliament before they are due to start on July 1.
Opposition finance spokesman Jim Chalmers said the first stage was important because it delivered cuts directed at low and middle income earners.
"The government should not be playing political games by saying it's all or nothing," he said.
"They're holding low- and middle-income earners hostage to tax cuts at the higher end of the income scale."
However, Labor was prepared to consider the rest of the plan "in due course", if more details were provided on the cost.
The tax cuts, which from July 1 include a low and middle-income tax offset of up to $530, will cost $13.4 billion over the first four years. The whole package will amount to $140 billion over a decade.
Also from July 1, the 32.5 per cent tax bracket threshold will be increased to $90,000 from $87,000, which will save 210,000 people from having to pay 37 cents in the dollar due to bracket creep.
More changes are planned in 2024/25, when the government proposes abolishing the 37 per cent tax bracket altogether.
Asked in parliament on Thursday whether he was prepared to split the bill, just as the government did with its corporate tax cuts, Treasurer Scott Morrison challenged Labor to pass the whole package immediately.
"If they give leave, we'll be happy to debate this bill right now," Mr Morrison said in parliament.
"We'll pass it now, the whole thing."
Mr Chalmers said the prime minister was the only person standing in the way of the July 1 tax cuts.
Pauline Hanson, who holds three key votes in the Senate, says she is willing to support the first and second stages but not the third.
"You can't go to step three - it's too far down the track," the One Nation leader told Sky News.
Asked whether she would ask for a cut in the immigration intake in exchange for her support, Senator Hanson said she did not expect the government to meet her concerns.
Her party would provide its support on the basis that they were the "tax cuts that ordinary Australians need".
The Australian Greens won't support any element of the plan.