The Prime Minister's hopes for easy passage of his signature budget measures rest with a party leader he has met just once since the election - and left her completely cold.
Greens leader Christine Milne said she met Tony Abbott in his office late last year and was unimpressed with the result. She claimed Mr Abbott did not live up to his statements on protecting Tasmanian wilderness.
Senator Milne said she had not met government Senate leader Eric Abetz or any Coalition senators. ''None, as in zero,'' she said, adding there would be ''little point''.
She said Mr Abbott ''does not have the skills'' to negotiate with the minor parties and she did not trust him, making it difficult to discuss his policies.
The fraught relationship between the party leaders will become more significant in the weeks ahead.
Mr Abbott is still hoping the Greens will support several of his policies, including paid parental leave, the re-indexation of the petrol tax and tightening the means-testing of family payments.
The Greens have the power to decide whether these policies pass through the Senate to become law.
Given the increasingly dysfunctional relationship between Mr Abbott and the Greens leader, back-channel communications have been occurring between the Prime Minister's chief of staff, Peta Credlin, and Greens deputy leader Adam Bandt.
It is understood that as opposition leader Mr Abbott had an easier relationship with the previous Greens leader, Bob Brown, than he does with Senator Milne.
Senator Milne said that in her one meeting with Mr Abbott, he assured her there were no plans to remove the existing ''lock-ups'' protection for Tasmanian forests, and that he would only stop new areas of forest from being locked up.
But contradicting Senator Milne's understanding of their conversation, the Abbott government has since sent a proposal to the World Heritage Committee to excise 74,000 hectares of Tasmanian wilderness from heritage protection.
''So from the Greens' point of view, what is the point of a meeting with the Prime Minister when he tells you one thing in his office and then does the opposite?'' Senator Milne said.
A spokeswoman for the Prime Minister says Mr Abbott had met Senator Milne once and she had not sought a meeting since. The spokeswoman did not respond to Senator Milne's claim about the Prime Minister's statements on protecting the Tasmanian wilderness.
''The Prime Minister is always prepared to meet with leaders of other parties as required,'' she said. ''However, unlike the Gillard-Rudd government, we are not in allegiance with the Greens and will not be holding regular meetings.''
Senator Milne said that despite her opposition to the Abbott government's budget philosophy, the Greens would probably help two Coalition policies become law - paid parental leave and the re-indexation of the petrol tax.
Senator Milne said the Greens were considering supporting the Coalition's proposals to tighten the means-testing of family payments from income levels of $150,000 down to $100,000, but they needed to see more details. However, she is opposed to other Coalition budget policies - university fee deregulation, GP payments, pension and Newstart cuts, the Direct Action plan.
And unlike the deals that led to the Greens-Labor alliance in the last Parliament, Senator Milne said she would not entertain ''horse trading'' with Mr Abbott.