Unions have cited WorkChoices and other excesses of the Howard years in a bid to shame the Greens party out of a deal with Malcolm Turnbull over Senate voting changes.

And they're citing persuasive privately commissioned polling data to support their claim that Greens' supporters themselves would feel betrayed by their party teaming up with the conservatives to clean independents out of the Senate.

In a new development in the contentious debate, ACTU secretary Dave Oliver has written to Greens leader Richard Di Natale reminding him of what happens when a conservative government gains control of both houses of Parliament.

Appealing to the Greens leader's progressive tendencies, Mr Oliver warns that the government wants the changes to Senate voting in order to pull on an early double-dissolution election - an election in which there is an increased chance that Liberals will replace crossbench senators and perhaps jag a majority in their own right.