Milwaukee Mayor Tom Barrett’s first ad of the gubernatorial recall election in Wisconsin begins by asking the question, “isn’t it time to end the civil war in Wisconsin?” He was referring to Scott Walker and the war on public employees, but he could be referring to the battle among Democrats over the next month.

Though Barrett, the 2010 Democratic nominee for Governor, has racked up some impressive endorsements since entering the race, including Rep. Ron Kind and former Reps. Dave Obey and Steve Kagen (the biggest potential endorsement, from former Sen. Russ Feingold, isn’t coming: he’s staying neutral), he does not have the support of organized labor. In fact, the Wisconsin state AFL-CIO just endorsed former Dane County executive Kathleen Falk, joining AFSCME and the state’s main teacher’s union:

“After careful consideration and discussion with all recall candidates, the Wisconsin State AFL-CIO has endorsed Kathleen Falk for Governor,” said Phil Neuenfeldt, President of the Wisconsin State AFL-CIO. “Kathleen’s dedication to improving the lives of working people and strengthening our middle class communities are key reasons for her endorsement. She has dedicated her life working for and listening to the people of Wisconsin. Her style of clean, open and honest government is the type of leadership Wisconsin needs.”

“Kathleen Falk will be a champion for working families,” said Stephanie Bloomingdale, Secretary-Treasurer of the Wisconsin State AFL-CIO. “She will bring our state together so that we can get back onto the path of good job creation and a growing economy.”

It’s not said here, but labor has a particular beef with Barrett. They accuse him of applying the anti-union law, Act 10, to force public employees in Milwaukee to contribute more to pension and health benefits. It’s true that labor agreed to those changes at the time, even before Walker passed his larger law. But they have a problem with Barrett instituting it, among other issues during his time as mayor of Milwaukee. The state AFSCME affiliate even passed around a fairly dishonest audio clip showing Barrett appearing to advocate for the “split the bill” strategy that eventually enabled Republicans to pass the anti-union law.

The point is that unions do not feel that Barrett was totally on their side in that fight last year, which animated this recall. It’s telling that Barrett says in this initial ad that he would “fight to restore collective bargaining rights for teachers and public employees.” But unions have even taken issue with that. They’ve said that Barrett’s strategy for repeal, using a standalone bill, has less of a chance of success than the strategy Falk has advocated, which would be to attach it to a budget bill to force it through.

The problem for labor is that Barrett is favored in most polling in the primary against Falk, Secretary of State Doug LaFollette and state Senator Kathleen Vinehout. Labor would have to spend and probably spend pretty big to dislodge Barrett. And with a massively large recall general election campaign against Walker coming just a month after the primary, that would be unwise. So the question becomes whether labor will put their money where their endorsements are, on Falk and against Barrett.