Australians could be going to the polls on July 2 after the Senate shot down the federal government's attempt to restore the building industry watchdog.

The federal government was handed the trigger for a double-dissolution election after the Senate again rejected legislation to restore the Australian Building and Construction Commission.

The bills were defeated 36-34, with crossbenchers Jacqui Lambie, Glenn Lazarus, Ricky Muir and John Madigan siding with Labor and the Greens.

MPs and senators were recalled to Canberra by Governor-General Peter Cosgrove at Mr Turnbull’s request, in a constitutional move not used for 40 years, to consider the industrial reform bills.

Mr Turnbull has vowed to use a second rejection of the bills as a trigger for a July 2 election, insisting the construction industry needs a cop on the beat to stamp out misconduct following last year’s damning royal commission report into union corruption.

Attorney-General George Brandis said the government was prepared to take the Senate’s rejection of its union legislation to the Australian people.

But he insisted Australia wouldn’t really be in an election campaign until parliament is dissolved and writs for an election are issued.

The government still plans to deliver its budget on May 3.

Opposition Leader Bill Shorten said Labor was ready for an election, whenever it is.

“This will be a contest between Labor putting people first, and a Liberal Party looking after vested interests and the big banks.”

Senator Lambie said the government had never properly negotiated with crossbenchers.

“If I was going after your vote, you would be that sick of me in your face, you’d pretty much want to take me out,” she told ABC TV.

“I never felt like that with the minister.”

She said the ABCC was absolutely not a justifiable trigger for an early election – most people had no understanding of the legislation, nor any interest in it.

A double-dissolution election means both houses of parliament are dissolved and all seats are up for grabs – only half of the Senate would be up for re-election in a regular election.