Party leader Adam Bandt said Prime Minister Anthony Albanese had to "get serious" about the housing crisis and negotiate a deal that would see house prices decline rather than climb.
"Renters and first home buyers across the country are at breaking point, but Labor's housing policy will push up rents and house prices for everyone," Mr Bandt said.
"The time is ticking for the prime minister to stop bulldozing and let his ministers negotiate with the Greens to pass this bill."
Adam Bandt hopes a delay will force the government to consider amendments. (Mick Tsikas/AAP PHOTOS)
Help to Buy would give 40,000 first-home buyers access to cheaper deposits through a shared equity scheme with the federal government.
A vote on the bill will have to go ahead on November 26, whether an agreement has been reached or not.
The Greens are also opposing the government's Build to Rent bill, which would provide tax incentives for developers who build new housing stock to rent out, rather than sell on.
Greens housing spokesman Max Chandler-Mather said the negotiations could be Labor's last opportunity to help renters and first home buyers before the federal election in early 2025.
"It is desperately cruel of Labor to pretend Labor's two bills will help, when one locks out 99.8 per cent of renters and drives up house prices for everyone, and the other gives tax breaks to developers to build expensive apartments they already planned to build," he said.
The Greens want the government to amend its housing reforms with a cap on rent increases, further investment in public housing and a phase-out of tax handouts for property developers.
Mr Albanese maintains the bills "stand on their own merits" without amendments, and has not ruled out dissolving parliament and calling an early election if the legislation fails to pass.
The coalition believes home buyers don't want the government to be part-owners. (Mick Tsikas/AAP PHOTOS)
Housing Minister Clare O'Neil said a double dissolution was a decision for the prime minister, but noted her government had a lot of work to do.
"We're not going to be stopping our agenda on housing because of these politicians playing politics," she told Nine's Today show.
"They should be putting politics to the side and letting our government get on with the job of helping Australians.
"It is just beyond me why a bill as straightforward as this is not getting the support of the parliament."
The coalition is also standing against the bill, with opposition finance spokeswoman Jane Hume claiming Australians will not sign up.
"It allows the government to own a great big chunk of your home," she told Seven's Sunrise program.
"Australians don't want that.
"They want to be able to own their own home."
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