Malcolm Turnbull will seek to head off election flashpoints and find new battlegrounds when he meets with state and territory leaders on Friday.
The premiers and chief ministers, meeting with prime minister as the Council of Australian Governments, are demanding long-term funding for schools and hospitals.
The prime minister, who will host the last COAG meeting before the federal election expected in July, won't be offering the guarantee.
However, he will put up to $5 billion on the table for public hospitals as an interim deal while a new mechanism is found for long-term funding.
Labor says the money won't cover the $7 billion cut from hospitals from 2017-2019 outlined in the 2014 budget.
Mr Turnbull's proposed way forward is allowing the states to levy income tax, ensuring the level of government that runs the services also funds the services.
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Health Minister Sussan Ley says the government's interim offer on hospital funding should satisfy the states.
"We won't necessarily walk away into the sunset, but a lot of the argy-bargy will stop," Ms Ley said.
"It will be terrific to get out of the other side of tomorrow."
While preschool education, science and technology teaching and teacher quality is on the formal agenda, there is no sign of a breakthrough on long-term schools funding.
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Mr Turnbull on Thursday argued there was a strong case for the federal government - having handed over some income tax powers - to no longer fund state schools from 2017, while maintaining responsibility for private schools.
"If the states decide they don't want to take responsibility, if they want to continue coming to Canberra and complaining, then ... that will affect the judgment Australians have of the states that do that," he said.
Queensland Labor Premier Annastacia Palaszczuk said she was disappointed schools funding was off the agenda, especially as the prime minister's economic agenda was all about innovation.
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"Innovation is driven by education," she said.
"The Abbott government cut $6 billion to future funding for education in Queensland. The Turnbull government needs to restore the funding."
She said instead she expected Mr Turnbull would attempt to "lecture" the states about his ideas.
Asked whether he thought Mr Turnbull was looking for a quick political fix before the election, NSW Premier Mike Baird said he understood the "challenging position" facing the prime minister in terms of the federal budget.
Labor leader Bill Shorten said he expected the tax idea to "die" on Friday, but would be happy to fight an election opposing a state-imposed income tax and proposing better federal funding of schools and hospitals.
COAG is also expected to discuss productivity payments for the states, domestic violence, medicinal cannabis and national security.
