Weatherill told reporters after the meeting that the Federal Government’s concessions on health funding amounted to a “moderate contribution” which would make up for 18 per cent of the cut to South Australia’s health system in the 2014 budget.

“If we are to be a first class nation we need to a first class health and education system,” he said.

“These should be the first calls on the nation’s finances, not the last call.”

He said SA remained “at odds with the Federal Government” on health funding and warned that “there’s a revenue problem in this nation”.

“This expenditure is locked and loaded – these people are coming into our hospitals,” he said.

Weatherill said there had to be “a substantial discussion” of the tax take “at some point”.

Prime Minister Malcolm Turnbull  agreed to provide the states with an extra $2.9 billion in funding for public hospitals and conceded states would not be levying income tax.

As part of the agreement reached at the Council of Australian Governments meeting in Canberra this afternoon, the states have committed to making improvements to the way hospitals are run.

The final communique said there was no consensus among the states to support “further consideration of the proposal to levy income tax on their own behalf”.

However, an alternative proposal to share personal income tax revenue would provide the states with a broad revenue base growing in line with the economy, reduce the number of tied grants and give the states greater flexibility in their spending.

Turnbull said discussions on new school funding arrangements would be concluded in early 2017.

He said all governments had a serious structural budget problem.

“We have to be clear-eyed about our choices – how do we get improvements to our infrastructure and central public services when there are more demands on government but less revenue available to pay for it,” Turnbull said.

He said the hospital agreement would run from July 1, 2017, to June 30, 2020 after which longer-term arrangements would be put in place.

Going into the meeting, the states understood the offer was only going to be six per cent.

Under the tax arrangement, the states would get control of a portion of income tax – possibly two percentage points from each tax bracket, equating to about $14 billion – but lose an equivalent amount in federal government grants.

If they need more money for services they would have to raise the rate.

Opening the Council of Australian Governments meeting in Canberra today, Turnbull encouraged the premiers and chief ministers to have a “rational and considered” discussion on improving the federation.

“We’re not here to make promises which we cannot afford,” he said in his opening remarks.

Premiers and chief ministers dined together in the Lodge last night ahead of the formal meeting today, with SA Premier Jay Weatherill describing the discussions as “positive”.

He suggested COAG was an opportunity to settle some form of recompense for the notorious withdrawal of forward funds for health and education in Joe Hockey’s 2014 budget, while finding consensus on a future “growth fund” to match projected increases in health spending.

Turnbull has proposed that states set their own income tax requirements, while Weatherill has requested a fixed share of Commonwealth income tax receipts.

“I don’t think the whole question will be entirely solved but I think it is possible for us to get a contribution towards restoring some of those cuts to health and education,” Weatherill told reporters.

“If we can achieve those things it will be a step forward, but it will still be only a small contribution to what’s a very big challenge.”

But the federal Opposition says the COAG agenda represents a “trifecta of bad ideas” by the PM.

The Government has floated a more generous education funding deal – if the states agree to be more accountable for their schools.

Weatherill has previously spoken about the notion that “states should have the entire responsibility for whole world of schooling from birth all the way to high school”.

“The Commonwealth should have responsibility for the world of work, which is everything beyond that,” he told FIVEaa this week.

“That would be a sensible demarcation of responsibility and would stop a lot of duplication.”

But other Labor premiers say they’re horrified by any proposal that would result in the federal government no longer funding state schools.

Shorten attacked the government’s education proposal as “the most outlandish idea in the history of Australian school education” while labelling health funding proposals a “Bandaid” solution.

“Mr Turnbull’s now come up with a trifecta. He’s completed a trifecta of bad ideas for the future of Australia,” he said.

– Tom Richardson and Bension Siebert with AAP