With the fate of two crucial crossbench seats in doubt, the federal government has left its legislation to restore the building watchdog off next week's Senate agenda.

The draft program, released on Wednesday, includes bills for the same-sex marriage plebiscite, backpacker tax and changes to vocational loans.

But there is no mention of the bills to re-establish the Australian Building and Construction Commission, the trigger for this year’s double dissolution election.

The Turnbull government has relied on One Nation and Family First to get its legislation through the tightly held upper house.

But Family First’s Bob Day won’t be in the upper house when it reconvenes on Monday after announcing his resignation, while One Nation’s Rod Culleton has indicated he will not vote on any contentious bills while his matter is being investigated.

Nevertheless, the government’s Senate leader George Brandis said the coalition was committed to its “very full” legislative agenda in the final three sitting weeks of the year.

“The government will be undeterred in prosecuting its agenda,” he told ABC’s 7.30 program.