* Republican Scott Walker faces voters in swing state
* Union restrictions he enacted prompted rare recall vote
* Barometer of political climate ahead of presidential election
* Test of strength between unions and conservative opponents (Updates with CNN exit polling data)
By Nick Carey
MILWAUKEE, June 5 (Reuters) - Wisconsin voters turned out in force on Tuesday to decide whether to throw Governor Scott Walker out of office in a rare recall election forced by opponents of the Republican's controversial effort to curb collective bargaining for most unionized government workers.
The rematch with Milwaukee's Democratic Mayor Tom Barrett, whom Walker defeated in a Republican sweep in 2010, is the end of six months of bitter fighting in the Midwestern Rust Belt state over union restrictions Walker enacted.
The recall election in closely divided Wisconsin, which helped elect Democrat Barack Obama as president in 2008, is seen as a barometer of the U.S. political climate going into the presidential election in November.
The vote is also viewed as a test of strength nationally between organized labor and conservative opponents, both of whom have poured money and effort into the contest.
Surveys of voters who had cast their ballots suggested the outcome would be close, CNN said. Wisconsin voters were equally unhappy with Republicans and Democrats. Some 88 percent said they made up their mind before May, when millions of dollars in campaign spending flooded the state to try to sway voters, the network said.
Voting was brisk on Tuesday in clear, sunny weather, with lines forming at polling stations across the state.
"I'm very excited. I'm praying and hoping, praying and hoping," said Willy Franklin, 65, a Barrett supporter in Milwaukee, as he stuck an "I voted" sticker to his jacket.
Roberta Komor, 53, of the Milwaukee suburb of Wauwatosa, said she had voted for Barrett when he ran in 2010, but this time voted for Walker.
The law firm secretary said that in today's hard times, unions "need to learn about shared sacrifice" when workers in the private sector have seen their benefits or wages cut.
"They have had everything handed to them on a platter," Komor said. "They need to be on a par with the rest of us."
Many voters seemed relieved the election had finally come, and voiced disgust with the recall process.
"There are too many recall elections that have been going on in the state and it needs to be stopped," said Carolyn Gral, 51, a Walker supporter and homemaker who is looking for a job.
Wisconsin held nine recall elections for state Senators last year after the union law was passed, setting a U.S. record.
This will be just the third recall election of a governor in U.S. history and it follows weeks of vociferous protests by demonstrators who occupied the state Capitol in Madison as Walker and fellow Republican lawmakers pushed through the union curbs in March 2011.
The law forced most state workers, including teachers, to pay more for health insurance and pensions, limited their pay raises, made payment of union dues voluntary and forced unions to be recertified every year.
Democrats and unions gathered nearly 1 million signatures to force the recall election. Politicians across the nation are watching the outcome closely.
"It has implications for the presidential race and national politics. Wisconsin could be a swing state," said Steven Schier, political analyst at Carleton College in Northfield, Minnesota.
If Walker wins, Schier said observers will forecast Republican chances in the Nov. 6 general election by measuring his margin of victory against his nearly 6-percentage-point win over Barrett in 2010.
Walker has led Barrett narrowly in most opinion polls leading up to the balloting, with very few voters undecided, so each side has mounted intense get-out-the-vote campaigns.
Opponents of the union curbs charge Walker and fellow Republican lawmakers undercut workers' rights. In Madison, where massive protests against the union law began, a rally outside the state Capitol on Tuesday drew hundreds of Walker opponents.
They sang "Roll Out the Recall," to the tune of the polka anthem "Roll Out The Barrel," in a festive, party atmosphere.
Passions are just as strong among Walker supporters who believe the changes were necessary to reduce a yawning budget deficit and curtail the power of government unions.
Walker voted in Wauwatosa, and he chatted with the voters while he waited in line.
He said in recent days many voters had come up to him to say they "appreciated that someone was willing to make the tough decisions."
"Tomorrow we have to work out how to move the state forward and get everyone back together," Walker said.
Walker's lieutenant governor, Rebecca Kleefisch, and three Republican state senators also face recall elections on Tuesday. A fourth state senator targeted for recall resigned, and a candidate from each party is vying for her empty seat. The state Senate is now evenly divided so a Democratic victory in just one of those races would hand them a majority.
Polls close at 8 p.m. CT (0100 GMT) but meaningful results are not expected immediately.
In 2008, Obama won Wisconsin by 14 percentage points over Republican John McCain. Two years later, Republicans roared back, electing Walker to replace the outgoing Democratic governor, defeating veteran Democratic U.S. Senator Russ Feingold and taking over both houses of the state legislature.
Even Obama's campaign organization conceded on Tuesday that Wisconsin could go either way in November, giving Republican presidential nominee Mitt Romney hope of winning a state that has not voted Republican since the 1984 presidential election.
A loss for Walker would derail a rising Republican star who has knocked down talk he might become Romney's vice presidential running mate, whereas a Walker win would be a blow to unions that are a powerful Democratic constituency.
The only two previous recall efforts against sitting governors succeeded: Lynn Frazier in North Dakota in 1921 and Gray Davis in California in 2003.
"Truthfully, I don't believe Barrett will win, but I do believe the state senate will flip," said Barrett supporter Andrew Karls, 29, after voting in Milwaukee (Additional reporting by Brendan O'Brien and James Kelleher; Editing by Andrew Stern, Anthony Boadle and Cynthia Osterman)