MADISON, Wis. — Even with the biggest name in modern Wisconsin politics, the Republican primary in a highly competitive U.S. Senate race appears headed for a fractious four-way battle Tuesday. Many election-weary voters simply haven't made up their minds.

Tommy Thompson, the former governor and Cabinet secretary, has near universal name recognition in the race to succeed retiring Democratic Sen. Herb Kohl. A recent poll finds Thompson leading the GOP field, but nearly 1 in 5 voters hasn't settled on a nominee.

Thompson had expected an uncontested run for the nomination given that his history with the party dates back to his first election victory in 1966 and includes 14 years as governor. He also served as health and human services secretary under President George W. Bush. But the party has grown more conservative since he left the governorship in 2001, and his three challengers argue that they are more in touch with modern Republicans than the 70-year-old Thompson.

The campaigns are spending millions on television ads trying to sway undecided voters, and each candidate seems to appeal to a slightly different constituency. Thompson is the experienced workhorse with the most political ties. Former U.S. Rep. Mark Neumann is the tea party favorite. Eric Hovde is the political newcomer who made millions as a businessman. And Assembly Speaker Jeff Fitzgerald has the most direct ties to Gov. Scott Walker, who survived a high-profile recall election just two months ago.

One theory is that Wisconsin is enduring a political hangover after that recall election, which Democrats organized as payback for Walker's push to strip most public workers of nearly all their collective bargaining rights. And, the primary is a month sooner than it used to be to comply with federal law. The result: Only 20 percent turnout is predicted.

"Wisconsin has been the state of chaos and I think people needed a break after the recall election and just weren't paying attention, unfortunately," said Nancy Milholland, a co-organizer of the Racine Tea Party. "All of our time spent working and focusing on the recall election would have been directed at the United States Senate race. The recall sucked the air out of the room."

The winner of the Republican race will take on Democratic U.S. Rep. Tammy Baldwin, who is uncontested. No Republican has held the seat since 1957 – the demagogic Sen. Joe McCarthy of "McCarthyism" infamy – but the GOP sees it as a pickup opportunity as they try to wrest majority control from the Democrats.

Keith Best, a salesman from the Republican stronghold of Waukesha, acknowledges that the recall took attention away from the primary but says he's undecided because all four candidates are strong.

"I probably won't make up my mind until I walk into the poll that Tuesday," Best said. "Game Day decision."

Republican voters are getting few cues from the state's most powerful GOP officer holders. Both Walker and U.S. Sen. Ron Johnson have refused to throw their support behind anyone in the primary, fearing they'd create divisions in the ranks heading into the November matchup with Baldwin, who has been in the House since 1999.

As much as they've tried to differentiate themselves, primarily through television ads, the candidates largely agree on major issues. All have focused their campaigns on their disdain for President Barack Obama's health care overhaul and what they see as the need to rein in government spending and reduce the debt.

A poll released on Wednesday by the Marquette University Law School found Thompson with an 8 percentage point lead over Hovde, which was just within the 4.4 percentage point margin of error. That, coupled with the number of undecideds, has the campaigns, observers and voters bracing for a late night.

"Hovde had a great start, Neumann's having a good close, and Tommy's Tommy," said Republican strategist Mark Graul. "I think it's going to be incredibly close."

Thompson is counting on his name recognition to resonate with people who haven't made their choice.

"No one has run a state government, and no one has won the state not once but five times," Thompson said. "There's no question in my mind I'm the best candidate."

Hovde is making the most noise, spending at least $4 million of his own money on a steady stream of ads that make the case for his fiscal conservatism and attack Thompson and Neumann.

The outsider businessman approach was successful for other Republican candidates in 2010 such as Johnson, Michigan Gov. Rick Snyder and Florida Gov. Rick Scott. Hovde said he models his campaign on that of Johnson, who also came out of nowhere and managed to knock off Democratic Sen. Russ Feingold.

Hovde worked as a hedge fund investor for 24 years in Washington, experience that his opponents attack. They also point to a spotty voting record and business deals with the government that appear to run contrary to his anti-spending rhetoric.

"I'm taking my hard-earned money because I care about my country passionately and I'm worried it's going to go through a financial collapse," Hovde said. "And I'm being criticized for making a big investment that's a giant negative return for me?"

Neumann, who spent four years in Congress in the 1990s, has the most support from tea party groups including the Tea Party Express, the conservative Club for Growth, and U.S. Sens. Jim DeMint, R-S.C., and Rand Paul, R-Ky.

Polls suggest Neumann has surged in recent weeks, putting him in position to pull a surprise in Wisconsin similar to the one engineered in Texas by Ted Cruz. A tea party candidate, Cruz shocked the Texas Republican establishment with his win last month in the GOP Senate primary.

Fitzgerald, a close ally of Walker's who helped push his conservative agenda through the Legislature, lagged in fundraising and in the polls.

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