Negotiations on the federal government's key housing proposal are set to continue into budget week as the Greens push for extra measures to address the housing crisis.
Vulnerable people urgently need a $10 billion housing fund to get over the line in the nation's "single biggest investment" in more than a decade, Housing Minister Julie Collins says.
But the Greens are calling for major amendments to the government's proposal to secure their support, including more rental assistance and one million new homes built to address the housing crisis.
The minor party is continuing negotiations with the government and movement on the bill is not expected until the next sitting week, which coincides with the federal budget in May.
Labor's election pledge would finance the construction of 30,000 affordable homes, but the Greens said this would be far outweighed by demand and would not address the housing crisis.
With one third of Australians living in rentals, the Greens said more assistance in the bill was needed for that group.
But Ms Collins said people at risk of homelessness needed the legislation to pass parliament.
"It is the ... single biggest investment in social and affordable homes in more than a decade," she told ABC radio.
Ms Collins said the government was doing its fair share to tackle the housing crisis, and issued a blunt message to those opposed to the bill.
"I would say to the Greens and to other crossbenchers in the Senate that vulnerable people cannot afford for this to delay," she said.
"If their response is 'it's our way or zero', that is just unacceptable when you've got vulnerable people on the ground who need housing today."
The fund would be established along with the independent Housing Australia body and a National Housing Supply and Affordability Council, which would provide independent advice.
But after the coalition confirmed it would not support the future fund, the government needs the votes of the Greens and two other crossbenchers.
ACT independent senator David Pocock won't support the bill in its current form.
Greens leader Adam Bandt said the policy was inadequate, and did not address rent hikes.
"At the end of Labor's plan, that waiting list for social affordable housing is going to be longer than it is at the start," he told ABC radio.
"We are pushing them to address the scale of the rental crisis that we're facing in this country and to step up and increase their offer."
CFMEU spokesman Zach Smith said the government needed to spend more money on its housing fund, or risk it failing.
"A more ambitious investment is a massive long-term opportunity for Australian jobs and industry but it needs to come with a commitment on local procurement and training," he said.
Senator Pocock will join Greens housing spokesman Max Chandler-Mather, and unions outside parliament for a rally on Tuesday, calling for a greater commitment from the government.
Peak housing and homelessness advocacy bodies have joined forces to call on the parliament to urgently pass the bills and start tackling the housing crisis.
Census data released last week showed there had been a five per cent increase in the number of Australians experiencing homelessness.
Analysts from the City Futures Research Centre at the University of NSW found 640,000 Australians are currently in housing stress.
By 2041, that number is expected to be one million.
National Shelter chief executive Emma Greenhalgh said Australians were paying the price with plummeting housing vacancies and skyrocketing rents.