Labor's likely victory after a four-year battle led the opposition to accuse the government of ``betraying'' the Australian people because it had promised before the 2007 election not to touch the subsidy.

The government is set to means test the 30 per cent private health insurance rebate and, at the same time, increase the Medicare levy surcharge for those without cover.

Health Minister Tanya Plibersek said she wouldn't wheel and deal with the Greens but she's nevertheless confident the reforms will get through.

``I do expect to see extra investment in the area of dental but what I'm not going to start doing is horse trading on this legislation,'' Ms Plibersek told ABC Radio.

``This is a very important piece of legislation and I think it will pass because of the merits of the case.''

The Greens back means testing the rebate but are opposed to increasing the surcharge because, they argue, people shouldn't be forced to take out private cover.

While the minor party could block the second of the two measures in the upper house, Greens leader Bob Brown says his members will ``concede'' on the issue if Labor puts the money raised by increasing the surcharge into dental care.

That's just $165 million over three years to win support for a reform Labor claims will save $100 billion by 2050 and at least $2.4 billion in the first three years.

Earlier in the week the Greens were demanding a $1 billion investment in dental care.

The government needs an extra three votes and is likely to get them from the Greens' Adam Bandt and independents Rob Oakeshott and Andrew Wilkie.