But critics say Labor hasn't offered any wiggle room in negotiations.
Prime Minister Anthony Albanese will be looking to put pressure on the coalition and Greens to pass two signature housing reforms during a visit to Sydney, where he will meet a homeowner who used a government program to get into the market.
Labor's schemes before the Senate - Help to Buy and Build to Rent - have faced criticism that they wouldn't make housing affordable.
The Greens are calling on the government to cap rent increases, increase investment in public housing and phase out tax handouts for property investors, but MP Max Chandler-Mather said the Commonwealth would rather let its bill fail than fight with the minor party.
"We recognise we're not going to get everything in our negotiation with the government," he told ABC on Tuesday.
Max Chandler-Mather says the government's plan would make housing more affordable for a select few. (Lukas Coch/AAP PHOTOS)
"But right now they've offered nothing - literally no counter offer.
"That's very frustrating when we're in such a serious housing crisis."
Mr Albanese said boosting supply levels was the best way to solve affordability issues.
"When I was young, more than two-thirds of Australians in their early 30s could buy their own home, now it's less than half," he said.
"The outlook is even worse for young Australians on low and middle incomes.
"That trend is only going in one direction unless we work together to do something about it."
The Help to Buy scheme would reduce the requirements for deposits for first-home buyers through a government loan guarantee.
Anthony Albanese says buying a home should be a "rite of passage". (Bianca De Marchi/AAP PHOTOS)
It's estimated 40,000 Australians would be able to buy their first property through the government program.
But Mr Chandler-Mather, alongside some economists, say the scheme would make housing more affordable for a select few, while pushing up prices for everyone else.
"It's desperately cruel for the government to hold this out as some sort of solution to the housing crisis," he said.
Coalition home ownership spokesman says the Commonwealth's shared equity scheme gives up on the Australian dream.
"Australians need to own houses, not the government," he told ABC radio.
A similar program, the Home Guarantee Scheme, had already been used by 120,000 people, among them the homeowner being visited on Tuesday by the prime minister.
Mr Albanese said parliament had an opportunity to expand housing access.
"Australians want to own their own home, parents want their kids to be able to enter the housing market," he said.
"Australians want solutions.Â
"It's time for the coalition and the Greens to stop blocking so we can get on with building more homes."
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