* 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 (Adds comments from polling places)
By Nick Carey
MILWAUKEE, June 5 (Reuters) - Wisconsin voters decide on Tuesday 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, who Walker defeated in a Republican sweep of the state in 2010, is the end-game of six months of bitter fighting in the Midwestern Rust Belt state over the union restrictions Walker proposed and 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 between organized labor and conservative opponents, both of whom have poured money and effort into the contest.
Voting was brisk Tuesday morning in clear, sunny weather, with lines forming at polling stations across the state. Many voters seemed relieved the election had finally come, and voiced disgust with the recall process.
"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."
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.
The measure angered Democrats and unions, who gathered nearly 1 million signatures on petitions to force the recall election.
"This is going to be an early indication of which way the political wind is blowing in Wisconsin," said Steven Schier, a political analyst at Carleton College in Northfield, Minnesota. "It has implications for the presidential race and national politics. Wisconsin could be a swing state."
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.
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 himself voted in Wauwatosa just after 7 a.m. Dressed in a light blue shirt and tan slacks, he seemed relaxed and chatted with the voters while he waited in line.
"For us, I think turnout is key today," he told reporters after voting. 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.
Walker has traveled the country and raised some $30 million for the campaign. More than half came from donors outside the state, including brothers David and Charles Koch, the conservative owners of the conglomerate Koch Industries. Barrett raised about $4 million.
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.
The outcome of Tuesday's vote will be claimed as a momentum builder by either presumed Republican presidential nominee Mitt Romney or Obama, analysts predicted.
Obama Tweeted on Monday "It's election Day in Wisconsin tomorrow, and I'm standing by Tom Barrett. He'd make an outstanding governor." Romney has called Walker a "hero."
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 could devastate unions that are a powerful Democratic constituency.
Only two previous recall efforts against sitting governors have ever made it to the ballot: Lynn Frazier in North Dakota in 1921 and Gray Davis in California in 2003. Both lost.
"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. Karls was wearing a bright red T-shirt with a blue fist on it -- an emblem of the fight against Walker.
"I'm confident that the rubber stamping that is going on in Madison with the Walker administration will stop," he said. (Additional reporting by Brendan O'Brien and James Kelleher; Editing by Mary Wisniewski, Andrew Stern and Anthony Boadle)