Labor’s Help to Buy housing scheme will support 40,000 eligible buyers with an equity contribution of up to 40  per cent for new homes, and 30 per cent for existing homes.

The government aims to have the scheme operating this year, but the Senate has referred the legislation to an inquiry which will report back in mid-April.

The Greens are demanding tax breaks given to property investors be significantly scaled back in exchange for their support for a plan they describe as Labor’s “housing lottery”.

Changes would be made to negative gearing and capital gains, with the saved revenue to be set aside for public housing.

The Greens will also continue to push for a rent freeze.

While no specific numbers have been provided to Labor as part of their ultimatum, the Greens have proposed limiting negative gearing rules to a single investment property.

Treasurer Jim Chalmers on Sunday ruled out changes to negative gearing and capital gains.

Greens leader Adam Bandt said his party would push to end “tax handouts for big property investors”.

“The system is stacked against renters and first home buyers, and Labor’s answer is a housing lottery for a lucky few and higher rents and house prices for everyone else,” he said.

Greens housing spokesman Max Chandler-Mather said his party would not stop fighting for renters.

“If Labor ignores us they will lose at the ballot box,” he said.

The government needs the support of the Greens and at least two crossbenchers for legislation to clear the upper house.

Shadow treasurer Angus Taylor said the coalition wouldn’t support changing the tax rules.

Negative gearing allows investors to claim deductions on losses, while the capital gains tax discount halves the amount of excise paid by people who sell assets that have been owned for 12 months or more.

As the focus on tax reform shifts to property investors, former NSW premier Dominic Perrottet has called for negative gearing to be reviewed as part of a wider debate about how changes could address housing affordability.