By Kat Wong, Andrew Brown and Jacob Shteyman in Canberra

The first hurdle to an early election has been cleared after the Albanese government failed to ram its housing laws through parliament.

For the second time, Labor was unable to pass its Help to Buy bill – which would give first-home buyers access to cheaper deposits through a government guarantee – in the Senate on Tuesday, ensuring the first trigger for a rare double dissolution election.

Only Jacqui Lambie voted with the government, with the coalition, the Greens, One Nation and UAP’s Ralph Babet torpedoing a motion to force on a vote.

“What a dysfunctional government was on display today,” said Liberal senator Slade Brockman

“They can’t run this chamber, how can they possibly run the country?”

A double dissolution occurs when there is a deadlock between the Senate and the House of Representatives on a proposed law, prompting the governor-general to dissolve both chambers, paving the way for an election.

If the government fails to pass the law through the Senate in another vote in at least three months from now, the double dissolution can be invoked.

Prime Minister Anthony Albanese earlier put pressure on parliament to pass the housing bill, along with another bill giving tax incentives for build-to-rent projects, a separate environment law overhaul and its Future Made in Australia bill, unamended.

“We’ll wait and see,” he told reporters in Sydney when asked if he would reach for the nuclear option.

“The way to avoid a (double dissolution) is for the coalition and the Greens to vote for legislation that they support.

“We’re always open to sensible discussions … but what we won’t do is undermine our own legislation with amendments when it stands on its merits.”

Greens party leader Adam Bandt called on the prime minister to continue negotiating, saying a double dissolution would be a “betrayal of every renter and first home buyer”.

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 amend its housing bills by including a cap on rent increases, further investment in public housing and a phase-out of tax handouts for property developers.

They also want to adjust the Nature Positive legislation to at least consider the impact mining and gas projects can have on climate change.

But the minor party says the government has refused to provide any wriggle room in negotiations and MP Max Chandler-Mather said Labor would rather let a key housing 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.

“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.

It’s estimated 40,000 Australians would be able to buy their first property through the Help to Buy scheme.

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 Andrew Bragg 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 been used by 120,000 people.