I thought Barrett was fighting for PUBLIC unions...

But no - he's snubbing the police to try and get the UAW - which lost workers in part due to Democratic "leadership" in Madison when GM shut Janesville down:
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When it came out last week that Milwaukee mayor (and Wisconsin Democratic candidate for governor in the upcoming recall election) Tom Barrett had skipped out on two ceremonies honoring Milwaukee police officers, there was some questions about what Barrett thought could possibly be more important that going to, say, a memorial service for slain Wisconsin policemen.  It probably didn’t help either that Barrett was so evasive about the answer, either – to the point of convenient memory loss.  Well, it turns out that Barrett probably wanted to forget the answer of where he was doing instead of honoring fallen officers, given that the answer was… ‘making a stump speech:’

…Mayor Barrett was actually speaking at a luncheon for retired United Auto Workers in Oshkosh at the exact same time that the fallen officers memorial was taking place in Milwaukee.  Barrett spoke to a room of about 50 UAW union members.

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Video at the link.

I still don't see why people in unions like UAW are against lower taxed for themselves, unless they have been thoroughly brainwashed into a "solidarity" mindset.