Labor is banking on the help of Greens MP Adam Bandt and independents Andrew Wilkie and Rob Oakeshott.

It appears all three may be willing to back the bills but it's not a sure thing, with the Greens indicating they could withdraw support if Labor makes too many concessions to the others.

The federal government admitted at the end of last year that it did not then have the numbers to pass the changes, which could save $100 billion by 2050.

Mr Oakeshott previously voted against the plan to means-test the 30 per cent private health insurance rebate and increase the Medicare levy surcharge for those without cover.

But yesterday, he was sounding positive.

He said he did not buy the ``Armageddon argument'' that private health insurers would lose vast numbers of members if the rebate was means-tested.

``I would fall on the side of the argument the government is presenting, rather than the private health industry, that there will be small drift,'' he said.

Mr Oakeshott will meet new Health Minister Tanya Plibersek early next week to seek ``solid assurances'' regarding his concerns over the impact on regional doctors and specialists.

Debate is scheduled to resume in Parliament on Thursday.

Labor is no longer guaranteed Mr Wilkie's vote after Prime Minister Julia Gillard reneged on her deal to introduce a mandatory precommitment scheme for poker machines by 2014.

But it is likely that he will still support the government in the end.

``Quite a bit of new evidence has emerged which I need to consider carefully before being able to confirm my support for the legislation,'' Mr Wilkie said.

But he added: ``If the settings aren't right, I won't support it.''

The Greens' position is nuanced. They support means-testing the rebate but not increasing the surcharge, which they claim will unfairly penalise those without private cover.

They also want to see Medicare-funded dental care and know the insurance changes could go a long way to funding that.

Their party room will decided a final position on Tuesday.