The prime minister and state and territory leaders are due to release the Council of Australian Governments communique on Friday afternoon.
NSW Premier Mike Baird went into COAG nominating infrastructure as his key priority, saying governments needed to set a target.
"It's the biggest economic lever we can pull," he told reporters before heading into the Parliament House meeting.
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It is understood he raised the issue in the meeting arguing for billions of dollars to be pumped into infrastructure.
Mr Turnbull answered: "We are not an ATM."
The federal government will release its mid-year budget review on December 19, which will show the impact of lower than expected wage growth, a stalling economy and other pressures on the bottom line.
The prime minister told reporters before the meeting he wanted homelessness and domestic violence to be priority issues for the meeting.
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The federal government has extended until June 2018 a partnership agreement with the states and territories for front-line services tackling homelessness.
"For many Australians who are homeless, who are lonely ... it's important we reach out to them," Mr Turnbull said.
On domestic violence, the prime minister said it was important the law was obeyed and prevailed.
"What we are doing is announcing that we will be changing the Family Law Act so that breaches of protection orders, injunctions to restrain conduct, contact and so forth will be a crime."
Mr Turnbull sidestepped questions about advice the government received from its chief scientist warning that Australia currentlyh has no clear path to meeting the 2030 carbon emissions target.
Security, affordability and meeting the Paris targets were the three goals Australia needed to achieve in a manner that kept downward pressure on electricity prices, he said.
"We are committed to ensuring keeping the lights on, that energy security is provided" Mr Turnbull said.
Mr Baird also wanted COAG to address what he says is a looming crisis on health funding.
Queensland Premier Annastacia Palaszczuk wants a national standard on domestic violence leave, as well as agreements on dental health and education.
"I hope that the prime minister has a few Christmas gifts for the states," Ms Palaszczuk said.
Victorian Premier Daniel Andrews said there was no good reason for the meeting not to agree to a national standard for family violence leave.
"Let's stop the talk, and let's get on and deliver," he told reporters, adding taking steps to protect women and children was his number one priority.
