The Albanese government's $10 billion Housing Australia Future Fund hangs in the balance, with the legislation failing to clinch the support it needs from crossbenchers in the upper house.
The Greens partyroom is on Monday expected to meet to decide its position on Labor's election commitment, which promises to build 30,000 new social and affordable homes.
Independent Senator Jacqui Lambie said discussions with the government were set to continue over the coming days.
"We're concerned about the set up and the way they have done their costs," she told Sunrise.
"This is also going to come down to once again the Greens, and whether or not they support it."
The government needs the Greens and two Senate crossbenchers for its legislation to pass the upper house.
ACT independent Senator David Pocock has also reaffirmed he won't support the bill in its current form.
