If Wisconsin were to redo its November 2010 gubernatorial election, Republican Gov. Scott Walker would lose to his Democratic rival Tom Barret, a new poll shows.

The results of a Public Policy Polling survey released Monday show that Barrett would beat Walker by a margin of 52-45 if the election were held now. Four percent said they weren’t sure.

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Walker, a first-termer, easily beat Barrett Nov. 2 by almost 6 percentage points.

The difference between how folks would vote now and how they voted in November mostly can be attributed to shifts within union households, the liberal polling service says. Voters who aren’t part of union households have barely shifted at all; they report having voted for Walker by 7 points last fall and they still say they would vote for him by a 4 point margin.

But in households with a union member voters now say they’d go for Barrett by a 31 point margin — up from the 14 point advantage they gave him in November, the survey says.

The shift toward Barrett is greater among Republicans than Democratic and independent voters. Only 3 percent of the Republicans surveyed said they voted for Barrett last fall, but 10 percent now say they would support the Democrat if they could do it over again.

Walker is embroiled in a bitter standoff with Democratic legislators over his proposal to curtail collective bargaining rights for most state employees. The dispute has led 14 state Senate Democrats to flee the state in a move to stall the proposal. And thousands of opponents of the governor’s plan have protested at the state Capitol the past two weeks.

The survey of 768 Wisconsin voters was conducted Thursday through Sunday.