* Milwaukee mayor leads Democratic primary candidates in polls
* Wisconsin voters focused more on jobs than unions
* Walker could become 3rd U.S. governor ever ousted
By Brendan O'Brien
MILWAUKEE, May 7 (Reuters) - Democrat primary voters on Tuesday may give Tom Barrett a second chance to face Republican Scott Walker in a historic recall election next month that will hinge on how the conservative governor has handled the state's struggling economy.
Polls show Barrett, the Milwaukee mayor, had a significant lead over Democratic candidates going into Tuesday's primary.
Barrett lost the Wisconsin governor's race to Walker by 5 percentage points in the Republican sweep of 2010. Since then, Wisconsin has been riven by what Barrett calls a "civil war" over Walker's drive to curb union power in the state.
"I want to be the governor who will restore trust in the government in this state, who will begin to heal the wounds that he opened ... and will end the civil war," Barrett said during a campaign stop in Stevens Point on Saturday.
Walker infuriated Democrats and labor organizations weeks after taking office in 2011 by pushing a measure that curbed collective bargaining power of public sector unions through the Republican-led legislature.
The measure requires public sector union members to pay a portion of their pension and health care benefits and caps wage increases. It also requires most public unions to recertify each year and makes it voluntary to pay union dues.
The law set off massive protests at the capitol in Madison. In January, Walker opponents submitted more than 900,000 recall petition signatures to the state elections board, triggering a Jun e 5 re call election of the governor.
"Democrats are so angry with Walker, this election is about the 'Not Walker' factor," said Timothy Dale, assistant political science professor at University of Wisconsin, Green Bay.
If he loses, Walker would become just the third U.S. governor to be removed from office.
Democrats surveyed by a Marquette Law School poll last week had Barrett at 38 percent, former Dane County Executive Kathleen Falk at 21 percent, Secretary of State Doug La Follette at 8 percent and state Senator Kathleen Vinehout at 6 percent. Nineteen percent of Democrats were undecided.
The same poll showed that if Barrett gets a rematch with Walker in the recall vote, they are in a virtual tie among registered and likely voters.
Almost everyone in Wisconsin has already decided what they think of Walker, leaving only 5 percent to 6 percent undecided.
The key to the outcome is likely to be which side does the best job of turning out its vote, analysts said.
JOBS, JOBS, JOBS
Surprisingly, the Walker attack on unions has not been the major issue of the campaign so far. Polls show Wisconsin voters, like those across the nation, are more focused on jobs.
Walker promised to add 250,000 new private-sector jobs in the state during his first term when he was campaigning for governor in 2010.
Democrats have hammered Walker since a U.S. Bureau of Labor Statistics report showed Wisconsin lost 23,900 jobs, the most for any state, from March 2011 to March 2012.
Vast amounts of campaign contribution money are flooding into the state with conservatives around the country supporting Walker and unions backing the Democrats. Walker has an enormous edge over Democratic challengers in fundraising.
Walker raised $13 million from January 17 through April 23, according to finance reports filed with Wisconsin - more than seven times the combined amount raised by Barrett and Falk.
The state's elections board expects voter turnout to be between 30 percent and 35 percent. This is high, compared to typical September partisan primaries in Wisconsin, which range from 9 percent to 25 percent turnout.
Wisconsin's unusual system means the vote on June 5 will not be whether to recall Walker but a choice between the governor and a Democratic opponent.
Republican Lieutenant Governor Rebecca Kleefisch and three Republican state senators, including former majority leader Scott Fitzgerald, also face recall votes because of their support of the union measure. (Editing by Greg McCune Doina Chiacu)