The federal government has failed to bring on a Senate vote that would have killed its own first home buyer support scheme, with the Greens and the Coalition voting together to delay consideration of the legislation for two months.

Labor's Help to Buy scheme, which would see the government co-purchase houses with 40,000 first home buyers, has been stuck in the Senate since February with no clear path forward.

Ahead of this week's Senate sitting, the government listed it for debate and has been trying to bring on a vote which it knows it will lose.

Government ministers have spent the week accusing the Coalition and the Greens of conspiring to block its housing agenda, but the government has in turn been accused of trying to kill off its own policy.

The Greens say they want the government to negotiate and have issued a long list of demands including negative gearing reform, a government-owned property developer and a rent freeze co-ordinated with states and territories.

But Finance Minister Katy Gallagher, who manages the government's Senate business, said the minor party was "not genuine about negotiating."

"[They're] talking about all these other things that are unrelated to the bill… It's time to get a vote on. If they're not going to support [Help to Buy], say so and frustrate our agenda."

Greens delay with Coalition support

On Tuesday afternoon, Greens leader Adam Bandt announced the party would move a motion to delay the bill for two months, which passed on Wednesday morning with Coalition support.

Mr Bandt said the delay was "a test for Labor."

"The Greens are willing to negotiate. The time is ticking for the prime minister to stop bulldozing and let his ministers negotiate with the Greens to pass the bill.

"This is a test for Labor. Do they want this bill to pass, or are they trying to make it fail?"

Senator Gallagher accused the Greens of playing a "procedural trick."

"Just be up-front that you're working…. with Peter Dutton and the opposition to frustrate what would be a useful housing program in the suite of our housing response to the housing shortage we have," she said.

"It's just another delay. And it's just disingenuous for the Greens to walk around [for] say two months and [suggest] they'll have some miraculous turn of opinion and support the bill. Like, if they oppose the bill, vote the bill down."

Bill forms part of broader housing agenda

The Coalition campaigned against Help to Buy at the last election and has argued Australians would not want the federal government to co-own their houses and that similar schemes at state and territory level are undersubscribed and "friendless."

The Greens have argued the number of beneficiaries is too small to make a difference to housing affordability and that supporting demand for housing will if anything push up house prices.

The government sees the measure as part of a broader suite of housing measures, including its tax incentives for Build to Rent apartment complexes – also stuck in the Senate – and its Housing Australia Future Fund (HAFF), which is set to support the construction of 13,700 social and affordable homes in its first funding round and more over time.

"We're committed, deeply committed, to dealing with the housing shortage in this country, and it's going to take a whole range of policy responses to deal with it. This is one of them," Senator Gallagher said on Tuesday.

"It's worth pursuing and also holding to account those that oppose it."

Prime minister dangles election threat

Prime Minister Anthony Albanese has threatened to use the Senate's obstruction of Help to Buy as a trigger for a double dissolution election.

That special category of election, which sees the entire Senate put up to the polls rather than the typical half-Senate election, can be called when the upper house twice rejects a government bill.

The government may regard this bill delay as a "failure to pass" and therefore the first rejection, as it did when a similar delay was applied to the HAFF bill.

A second rejection later this year could allow a double dissolution election to be called for late January.

That would not be expected to advantage the government, but Mr Albanese said "we'll wait and see" when asked about it on Tuesday.

While a double dissolution election is highly unlikely, the comments have fuelled further speculation about an early regular election, which the government can call at any time.