Premiers appear set to turn down an offer by Malcolm Turnbull to allow the states to levy a portion of income tax to fund schools and hospitals.
But they will take away from Friday's Council of Australian Governments meeting an interim deal on health care funding.
The prime minister, who is due to dine with the state and territory leaders at The Lodge in Canberra on Thursday night, has stepped up his argument for the states to take more responsibility for funding education and health.
Giving the states 2 per cent of income tax would provide them with about $14 billion in annual funding and save the federal budget an equivalent amount in grants that would be cut.
If the states needed more money, they would have to make their case to their own parliament and voters to raise the levy.
"This is really a test for the states and territories," Mr Turnbull said on Thursday.
"If they want to continue coming to Canberra and complaining then I think Australians will say 'Well, you had the opportunity to step up and be responsible and you knocked it back'."
Mr Turnbull's closest political ally, NSW Premier Mike Baird, said he wanted to see more evidence about how the change would work.
But NSW insists Mr Turnbull should commit to the Gonski model of school funding agreed under the former Labor government and guarantee hospital funding beyond the next decade.
"You cannot take billions and billions of dollars away and say 'It's your problem'," Mr Baird said.
Mr Turnbull said there was a "very powerful case" for the federal government to no longer fund state schools from 2017, while maintaining responsibility for private schools.
Australian Education Union deputy president Maurie Mulheron said it was a "betrayal" of state school students.
Queensland Premier Annastacia Palaszczuk said the income tax plan lacked detail and her state was facing a shortfall of $6 billion in education funding and $11.8 billion in health funding.
South Australian Premier Jay Weatherill said "double taxation" would not work.
Victoria's Daniel Andrews queried how a system in which no extra money was raised could pay for more services, just as the federal government was scaling back its funding by $80 billion.
Mr Turnbull hinted at "mechanisms" to cushion smaller, poorer states like Tasmania and South Australia so they were not disadvantaged.
Federal shadow treasurer Chris Bowen said it was an April's Fools joke by the prime minister.
The premiers won't leave Canberra empty-handed.
The prime minister is expected to put an interim health funding deal on the table which has been estimated at $5 billion across all states.
It would also commit the federal government to the idea of activity-based funding and a national efficient price for hospitals.
Health Minister Sussan Ley said the hospital funding deal was "a good one".
"The states will be happy with it. We won't necessarily walk away into the sunset, but a lot of the argy-bargy will stop," she said.
