Kevin Rudd is offering premiers an extra $1.2 billion to win support for his health plan but it remains contingent on a potential "showstopper" - handing over 30 per cent of their GST.
The additional funds, which will flow from July 1, 2010, would go towards elective surgery, emergency departments and new beds.
The Council of Australian Governments (COAG) meeting broke around 1600 AEST on Monday to give premiers and chief ministers time to consider the offer.
However the meeting has still not considered two key matters - pooled funding and the GST.
Mr Rudd is proposing the commonwealth would claw back about 30 per cent of states' GST revenue and, in return, the federal government would take control of 60 per cent of hospital funding.
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The GST is a no-go zone for Victoria, Western Australia and NSW.
Mr Rudd put on the table on Monday an extra $1.2 billion, including $150 million for elective surgery infrastructure, $250 million to expand capacity at public hospital emergency departments, and $827 million for more beds.
The elective surgery money would go towards elective surgery centres and day surgery centres.
The government also wants to free hospital beds by delivering more funds to palliative, rehabilitative, geriatric and mental health care services.
This is in addition to nearly $3 billion in sweeteners he offered states and territories in the lead-up to the meeting.
However, they have to sign up to his GST plan if they want the extra money.
West Australian Premier Colin Barnett acknowledged the federal government had been very generous.
"The commonwealth's been generous, that's been accepted," he told reporters.
"But there's still the two big issues to address."
Earlier Mr Barnett remained doubtful the impasse over the GST could be broken.
"Not unless the commonwealth agrees for the states to pay an equivalent amount of the GST, rather than take the GST off the states," he told AAP.
"The potential showstopper is the GST."
The public supports a breakthrough.
The latest Herald/Nielsen poll, published in Fairfax newspapers, indicated two-thirds of people wanted the states to strike a deal, while an Essential Poll had support at more than 50 per cent.
