Seth Perlman / AP Wisconsin Gov. Scott Walker is surrounded by the news media after speaking to the Illinois Chamber of Commerce Tuesday, April 17, 2012 in Springfield, Ill.

The battle of Wisconsin was never going to be cheap. Scott Walker, the Republican governor facing a landmark recall election next month, is perhaps the most polarizing politician in the country not named Obama. The June 5 election in a bitterly divided swing state is seen by both sides as a bellwether in the ongoing clash between Big Labor and Big Business, and each is flexing its financial muscles. “We’ve spent a lot of money in Wisconsin. We’re going to spend more,” David Koch told a reporter in February.

Walker will need it. With a month to go before voters swarm to the polls, the controversial governor is locked in a virtual tie with his likely Democratic opponent, according to a new poll from Marquette University Law School. Among likely voters, Walker holds a 48% to 47% edge in a hypothetical matchup with Milwaukee Mayor Tom Barrett; the one-point margin is reversed among all registered voters. Barrett, whom Walker defeated by five percentage points in the 2010 gubernatorial race, leads Dane County Executive Kathleen Falk, who boasts union backing, in polls ahead of the May 8 Democratic primary. The rematch would be a coin flip, says Charles Franklin, the Wisconsin political expert in charge of the Marquette poll.

(PHOTOS: Union Protests in Wisconsin)

Walker’s opponents gathered more than 900,000 certified signatures to recall the governor. But despite the grassroots groundswell, Democrats face an uphill fight. Thanks to election law and deep-pocketed, out-of-state benefactors like the Kochs, Walker boasts a substantial fundraising advantage.

Since mid-January, Walker’s campaign has raked in more than $13 million, according to financial disclosure statements released this week. During that time, two-thirds of his cash came from outside the Badger State. The record haul eclipses the $12.1 million Walker netted last year amid his high-profile clash with protesters, who were incensed by his successful push for a “budget repair” bill that curbed collective-bargaining rights for most of the state’s public employees. By contrast, Barrett reported raising $830,000, and Falk nearly $1 million. Walker spent almost $11 million over the past three months to stave off his challengers.

Walker’s tally was boosted by a state law that lets recall targets amass unlimited funds from the moment a group initiates the recall until a state board sets the date of the election. That period lasted some five months. Walker’s prolific fundraising, and the hefty sums heaped on the race from wealthy outside groups, have led some analysts to suggest the total tab for the race could approach $100 million, making it the most expensive campaign in the history of the state. Already the candidates and their allies have raised and spent some $42 million, according to a Milwaukee Journal Sentinel analysis of data compiled by the Wisconsin Democracy Campaign.

(MORE: Behind Democrats’ Million-Signature Show of Force in Walker Recall Effort)

In a press release touting its haul, Walker’s campaign pointed to its pool of more than 125,000 contributors — 76% of which gave $50 or less — as evidence of the governor’s “strong grassroots support.” There is no question Walker has an army of backers. But a close look at the people ponying up the cash reveals the degree to which the tussle is being funded by corporate titans from outside Wisconsin.

Walker’s biggest donors include Sheldon Adelson, the casino magnate who kept Newt Gingrich afloat and fed $250,000 to the first-term governor; Rich DeVos, the Orlando Magic owner and Christian conservative founder of Amway, who also kicked in a quarter-million; and Texas home builder Bob Perry, known for bankrolling Republican causes ranging from Mitt Romney’s campaign to Swift Boat Veterans for Truth, who gave Walker $240,000. Foster Friess, who earned renown as Rick Santorum’s benefactor, gave $100,000. Americans for Prosperity, funded by the conservative Koch brothers, shelled out $700,000 to run TV ads in Wisconsin. “We’re helping him, as we should. We’ve gotten pretty good at this over the years,” Koch told a reporter from the Palm Beach Post in February.

Labor unions opposed to Walker’s policies have funneled plenty of money into the fight as well, including some $4 million on behalf of Falk, the more liberal of the leading Democrat candidates. But Walker’s windfall boosts his chances in the critical ground war that will help swing the election in this bitterly divided state. Walker is the most polarizing governor in the U.S., according to surveys, and polls have shown that fewer than 5% of voters are undecided. Which means get-out-the-vote campaigns will be paramount.

“There are no persuadables,” says Mordecai Lee, a political science professor at the University of Wisconsin-Milwaukee, which means both sides’ tactics will be “Karl Rove’s 2004 strategy cubed: finding your niche demographic and getting them to vote.” Democrats demonstrated their passion for the race by descending on Madison to protest en masse last winter, and reaffirmed it through the resolve of their petition circulators. But Walker spent $4.6 million alone over the past three months on a direct-mail firm, according to the Journal Sentinel. That kind of financial organization can be tough to overcome.

The irony of the race is that while curbs on collective bargaining were the spark that kindled the recall, the issue has receded from both sides’ messaging as the election approaches. “It’s not front and center to the campaigns right now,” Franklin says. Instead, both sides are focusing on bread-and-butter issues: jobs and unemployment. Walker, who promised to create 250,000 jobs during his tenure in the statehouse, has been damaged by Bureau of Labor statistics that indicate Wisconsin has lost more jobs over the past year than any other state. At the same time, Wisconsin’s unemployment rate, hovering just under 7%, remains below the national average, and Walker’s campaign has claimed that the bulk of the job losses came under Barrett’s leadership in Milwaukee. The Journal Sentinel has thrown cold water on that argument.

Walker would be only the third governor in history to be recalled, following California’s Gray Davis in 2003 and North Dakota’s Lynn Frazier in 1921.