West Australian Liberal senator Dean Smith has challenged the Morrison government to broaden the GST or increase the rate to 12.5 per cent in return for eliminating state-based payroll taxes.

"Well, we're not doing it," Mr Morrison told reporters in Sydney on Monday.

The prime minister later elaborated.

"People know that some time ago we actively considered this, we examined it very carefully," he told Sky News.

"The sad truth was with something like that you had to spend half of what was actually raised in providing compensation for the implementation of the tax.

"So at the end of the day, the numbers just didn't add up."

Mr Morrison indicated any changes to the GST would have to be put to a public vote.

"The Australian people would have to have a judgment on that for that to occur, and so it's not on the agenda, we ain't doing it."

Senator Smith has encouraged state and territory treasurers to lobby their federal counterpart in support of the "politically courageous" tax shake-up.

"They could abandon their calls for a boost in infrastructure spending and increases to Newstart and instead stand united in a call for tax reform, which starts with the removal of payroll taxes in exchange for a broader-based consumption tax," he wrote in the Australian Financial Review.

He says payroll tax is a drag on economic activity and is "ultimately paid by employees through lower wages and higher prices for consumers".

"Compensating state and territories for lost revenue could be achieved by broadening the GST or by a modest (but politically courageous) lift in the GST from 10 to 12.5 per cent," he wrote.

Opposition Leader Anthony Albanese warned jacking up the GST would hit pensioners and families.

"This is a government that never misses a chance to hurt working people, and to redistribute income away from those who can least afford to pay more," he told reporters in Perth.

"The GST, by definition, is a regressive tax because it hits people at the same rate regardless of what their income is."

Meanwhile, the watchdog overseeing the Australian Taxation Office is launching an investigation into a $7 billion blowout in unpaid taxes.

Taxation Ombudsman Karen Payne wants to understand why the total undisputed tax debt has grown from $19.2 billion to $26.2 billion over the past four years.

"Where is it accumulating in the system? Is it in big business, small business, or other specific sectors within the economy?" Ms Payne told The Australian.

"We want to try and understand if there are particular taxes it is associated with -- GST, income tax, CGT (capital gains tax) or BAS-type (business activity statement) taxes.

"And then to use that scoping study to do a better, and more targeted, deep dive."

Australian Associated Press