but there are some union office holders who are left-wing. Senator Doug Cameron, formerly of the AMWU, is definitely a leftie, but mostly they seem to be controlled by the Catholic right-wing of the party. This is the main reason why former PM Julia Gillard opposed same-sex marriage - her own lifestyle and personality would seem to dictate that she would hold the opposite view, but the right-wing put her in power, and she couldn't cross them. They are vehemently opposed to marriage equality, especially the strong shopworkers' union, led by Catholic Joe de Bruyn. If she had defied them, she'd have been done like a dinner.
In my work, I have to liaise at times with the MEAA (Media, Entertainment and Arts Alliance), which comprises actors, entertainers, journalists, and backstage workers. Many of these people are Labor voters, and the union definitely leans to the left, but they're a rarity.
Here's a link to an article that came out prior to the election, in which Joe de Bruyn not-so-subtly threatens Kevin Rudd. For "Labor heartland", read "trade unions, especially mine".
http://www.theaustralian.com.au/national-affairs/election-2013/kevin-rudds-silence-on-gays-a-bid-to-save-votes/story-fn9qr68y-1226701643043#
Edit to add: The Australian is a Murdoch paper, so the content will always be anti-Labor.