The federal government’s plan to become a co-owner with thousands of Australians who are trying to buy a home is at risk of failure as the Greens threaten to shoot down Labor’s help-to-buy scheme.

The government proposes to help cover up to 40 per cent of the cost of homes for thousands of Australians and in return become a part owner, with homebuyers able to buy out that stake at a later date.

It would allow individuals earning less than $90,000 and couples earning less than $120,000 to pay just a 2 per cent deposit for a home.

But the Greens argue that with a limit of 10,000 applicants and price caps on eligible properties, it will only help about 0.2 per cent of buyers each year — and may further push up house prices.

The party says it will vote against the bill when it is put to a vote in the lower house, where the government holds a majority, and reserves the right to vote against it in the Senate where it has the power to sink the bill.

Greens housing spokesman Max Chandler-Mather said unless the government was prepared to introduce rent caps, build more public housing and wind back property investor benefits, the Greens would not support the bill.

“You can tinker around the edges on this bill, but you will not fix the housing crisis unless you deal with the billions of dollars in tax handouts for property investors,” Mr Chandler-Mather said.

“The prime minister has said when economic circumstances change then so should government policy.

Well, now they need to look at the fact the [Reserve Bank] has said rents will go up even faster this year than they did last year.”

Greens leader Adam Bandt said his party had previously been told the government that it was not prepared to budge, “and then they do”.

“We know pressure works,” Mr Bandt said.

The party argues that because the help-to-buy bill is the last housing policy the government announced before the election, this is the final chance to secure reforms it says are critical to easing pressure on renters and homebuyers.

Government says Greens and Coalition standing in way of support

The Coalition opposed Labor’s help-to-buy scheme at the 2022 election, arguing people could be forced out of their homes if pay rises pushed them above the income criteria and required them to pay back the government’s stake too early.

Deputy Opposition Leader Sussan Ley told Sky News the scheme would not work because house prices had already run past the eligibility thresholds.

“For you to actually be eligible in Sydney, the house price has to be $950,000,” Ms Ley said.

“I was in the west of Sydney in some very ordinary battler neighbourhoods where they told me house prices were $1.2 million.

“So I think a lot of people who are struggling right here right now will be unable to even get in the door with this policy.”

Without the Coalition’s support, the government needs the backing of the Greens to have any chance of passing its help-to-buy bill.