Coalition, Greens gag watchdog debate

A crossbench attempt to fast-track a Senate debate on restoring the building industry watchdog has been stymied by the government and the Greens.

Motoring Enthusiast senator Ricky Muir tried to bring on the debate, accusing the government of ignoring a measure it admits is a high priority.

But the coalition and the Greens used their combined numbers to quickly shut down the move on Tuesday.

The Greens also sided with the government to quash debate on its own same-sex marriage legislation.

Liberal Democrat David Leyonhjelm tried to bring the bill on for consideration this week, saying it would be "perverse and undemocratic" for the Greens to avoid consideration of their own bill.

Greens leader Richard Di Natale slammed the move, insisting there was no greater supporter of marriage equality in parliament than the Greens.

He challenged Labor to bring the matter on for debate on Thursday during the time allocated for private bills, to prove they weren't crying "crocodile tears".

Crossbencher Glenn Lazarus also tried to embarrass the government and the Greens by attempting to bring on the building industry watchdog debate as well as a Greens bill to allow landholders the right to refuse gas and coal mining on their land.

Labor Senate leader Penny Wong accused the government and Greens of prioritising their "dirty deal" on changes to Senate voting over their own core values.

The government's building watchdog laws weren't "quite as important as everyone said", she said.