Wisconsin Gov. Scott Walker and fellow Republicans on Wednesday hailed Walker's survival in a bitter recall election as proof that voters want leaders who take bold action to fix problems, even if the solutions aren't popular.

Walker won the Tuesday vote over Milwaukee's Democratic mayor, Tom Barrett, in a rerun of the 2010 gubernatorial election that produced the same result.

This time, it was Walker's steps last year to weaken public unions as part of austerity measures that prompted the recall effort waged by Democrats and organized labor.

The campaign set state records for spending, with Walker getting most of the tens of millions of dollars in outside money.

Both Walker and his lieutenant governor survived the election, along with three of four Republican state senators also facing a recall vote. Democrats claimed victory in the other state Senate race, which would give them a majority in the chamber.

The outcome showed that Wisconsin is in play in the November general election after President Barack Obama easily won it in 2008.

Although Obama still is considered the front-runner there over certain GOP nominee Mitt Romney, the organizing ability displayed by Republicans in defending Walker's position showed that the Wisconsin race will probably be more competitive this time around.

"Governor Walker has demonstrated over the past year what sound fiscal policies can do to turn an economy around, and I believe that in November voters across the country will demonstrate that they want the same in Washington, D.C.," Romney said in a statement, adding that the result "will echo beyond the borders of Wisconsin."

Obama's campaign released a statement praising those who worked on the recall.

"While tonight's outcome was not what we had hoped for -- no one can dispute the strong message sent to Governor Walker," the statement said. "Hundreds of thousands of Wisconsinites from all walks of life took a stand against the politics of division."

Barrett and other Democrats argued that Tuesday's result was unique to the state, caused in part by the huge money advantage for Walker supplied by outside interests.

"What you had was an incumbent governor in a repeat election that he had won once, in which he outspent his challenger by a magnitude of 7 or 8 to 1, with an enormous amount of outside corporate money and huge donations, and you got essentially the same result," White House Press Secretary Jay Carney said Wednesday.

Walker and Republicans, meanwhile, insisted that voters want leaders willing to make tough decisions to solve problems.

"The message that was sent was, voters do mean it when they say they want people to take on the tough issues," Walker said Wednesday.

He advised both Obama and Romney "to explain what they'll do, how they'll look out for the next generation more than just getting through this next election."

Virginia Gov. Bob McDonnell, who heads the Republican Governors Association, which strongly backed Walker's campaign, noted that Walker addressed difficult budget issues facing the country.

"He said 'we have a budget deficit and have to eliminate it without raising taxes,' and he did it," McDonnell said Wednesday.

In his victory speech Tuesday night, Walker addressed the polarized climate in the normally centrist state; the crowd jeered when he mentioned that he had a phone conversation with Barrett before taking the stage.

"Bringing our state together will take some time, there's just no doubt about it," he said.

Both Walker and Barrett pledged to work together to try to heal some of the political wounds, but it appeared unlikely much progress would occur anytime soon.

The recall effort against Walker was spurred by a law he backed and signed in March 2011 to limit the collective bargaining rights of state worker unions.

Walker and other Republicans complained that repeated recall efforts in Wisconsin over past years were stalling progress and costing the state needed money. They also said voters were tired of recall politics, a point on which AFL-CIO President Richard Trumka agreed.

"Many of our own members believe that recalls shouldn't be around for anything but corruption," Trumka said Wednesday. At the same time, Trumka said the fight for workers' rights would continue, declaring, "This is just the opening shot of a battle that is going to go on until November."

In the only bright spot of the night for Wisconsin Democrats, former state Sen. John Lehman declared victory over Republican incumbent Sen. Van Wanggaard in one of the four contested state races.

The outcome shifts majority control of the chamber to Democrats. However, the legislature will be out of session until after the general election in November that could again change the balance.

Barrett drew catcalls Tuesday night when he mentioned in his concession speech that he called Walker, but he urged his supporters to press on, declaring "this is not an end" to their fight.

A local woman was not amused by Barrett's concession speech, with video from CNN affiliate WISN showing her slapping the mayor after the speech.

The woman asked Barrett whether she could slap him for conceding while voting was still under way, the affiliate reported. Barrett said he'd rather she hug him, but when he leaned down, the woman slapped him instead, according to the affiliate.

The campaign was fierce, with participants complaining of keyed cars, verbal harassment and a general lack of tolerance for differing opinions.

"We have an example of Hatfields and McCoys going on in this state like we have never seen," said Brian Nemoir, a Milwaukee-based Republican strategist. "People are hyper-engaged, as much in support for their own candidate as in disgust for the opponent."

A number of Republican stars campaigned for Walker, including fellow Govs. Chris Christie of New Jersey, Nikki Haley of South Carolina, Bobby Jindal of Louisiana and McDonnell, as well as U.S. Sen. Marco Rubio from Florida.

Barrett, meanwhile, got his own high-powered support from former President Bill Clinton, as well as Democratic National Committee Chairwoman Debbie Wasserman Schultz and Maryland Gov. Martin O'Malley.

Obama never came to Wisconsin to campaign for Barrett, which Republicans surmised was because the president thought Barrett would lose. The president publicly supported Barrett.