Days after delivering his own budget, Mr Morrison said the Labor leader's response on Thursday night didn't have any solutions for the nation.
Later the treasurer said the cost over the "next" 10 years would be $65.4 billion.
The deficit levy is due to expire on July 1, three years after its introduction by Joe Hockey, and applied an additional 2 per cent tax rate to people earning more than $180,000.
The change would mean that taxpayers can not deduct more than $3000 in payments to lawyers or tax accountants for managing their tax affairs.
But Mr Shorten insisted his party was looking after middle-income households that would cop a Medicare levy increase under the coalition.
In power, it would reverse the government's new cuts to TAFE.
He said the 0.5% boost in the Medicare levy - imposed to fund the National Disability Insurance Scheme and to take effect from mid-2019 - would affect every Australian down to an income of $21,000.
The Deloitte analysis shows that 18.3 per cent of taxpayers earn more than $100,000 a year, and they will pay 46.5 per cent of the additional Medicare levy.
"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. Who's budget proposals do you like more?
He dismissed the government's measures to protect Medicare, saying that Malcolm Turnbull "only discovers his heart when he feels fear in it".
He confirmed Labor would not oppose the budget's tax on big banks, which has sparked a furious reaction from the banking sector.
Explosion at Mexico fireworks depot kills at least 14
Despite frequent and deadly accidents, data show Mexicans continue to spend about $10 million each month on fireworks nationwide. The fireworks were due to be used for the local patron saint's festival on May 15 and were stored inside a house behind a church.
They're facing a backlash from the bankers over the surprise $6.2 billion levy on Australia's largest financial institutions.
The banks knew they could run over the top of this weak prime minister, he said.
Treasurer Scott Morrison's second budget signalled the end to the two per cent budget deficit levy, which was temporarily put in place in 2014 to help balance the books.
In his budget reply, Shorten said: "This is a recipe for fiscal recklessness on a grand scale".
Labor will propose to set a limit on how much people can deduct for managing their tax affairs of $3000.
This, he will argue, is a rort and the change will hit less than 1 per cent of taxpayers.
Finance Minister Mathias Cormann called on Shorten to submit his speech to the Parliamentary Budget Office for costing.
'We are actually taking a stand for the eight million people who earn less than $87,000 a year, ' he told ABC radio.
"His numbers didn't add up".
Shorten said Labor would crack down tax evaders hiding funds in offshore accounts.