Opposition Leader Bill Shorten has said Labor will oppose the budget's increase in the Medicare levy hitting taxpayers on incomes under A$87,000.
Initially, Mr Turnbull - in answer to a question from Opposition Leader Bill Shorten - said the total cost of the 10-year plan was $26 billion.
The Coalition want to increase the Medicare levy by 0.5 percentage points for nearly all Australians, which would equate to an extra $375 a year for those earning $75,000.
"There's nothing fair about a $65 billion giveaway for big business while you're cutting $22 billion from schools", Mr Shorten said.
"Labor can not support making people on modest incomes give up more of their pay packet, especially when this budget goes out of its way to give taxpayer money to millionaires and multinationals", he said.
"At a time when the government is asking every other working Australian to pay a higher rate of tax, Labor will not support spending at least $1.2 billion each year on the wealthiest two per cent", Mr Shorten will tell parliament.
Labor has yet to confirm whether it will support the hike included in the 2017 budget which will cover a $3.8 billion gap in funding for the National Disability Insurance Scheme.
Treasurer Scott Morrison's second budget signalled the end to the two per cent budget deficit levy on taxable incomes over $180,000, which was put in place in 2014 and is due to expire on June 30.More news: Governor sentenced to prison for blaspheming Islam
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But it was anxious that "the weakness of this government will turn $6 billion tax on the banks into a $6 billion charge on every Australian with a bank account or a mortgage".
Elsewhere, Labor would cap the amount people can claim as a tax deduction for the management of their tax affairs at $3000 to stop people "exploiting holes" in the net.
Mr Shorten has accused Prime Minister Malcolm Turnbull of giving millionaires a tax cut by ending the levy.
The crackdown would reportedly raise $1.8 billion over a decade and would affect less than 1 per cent of taxpayers.
Analysis by Deloitte's Chris Richardson suggests that about 50,000 people with annual income of more than $1 million will contribute 6.9% of the increased revenue from the proposed 0.5% rise in the Medicare levy.
Finance Minister Mathias Cormann said Mr Shorten's speech was full of political rhetoric but short on a plan to grow the economy and create jobs.
Social Services Minister Christian Porter said that Labor had not outlined enough to fund the NDIS.