In this Dec. 1, 2011, file photo, former Wisconsin governor Tommy Thompson greets supporters after formally launching his bid for U.S. Senate, at a manufacturing facility in Waukesha, Wis. (Dinesh Ramde/Associated Press)

A month ago, many people in this state presumed that Tommy G. Thompson — still a household name here after serving an unprecedented four terms as governor — had a lock on the Republican nomination for the Senate.

Not anymore.

Wisconsin, which has seen more than its share of bare-knuckle politics over the past year, is the setting of an increasingly bitter three-way GOP Senate primary fight whose outcome later this month is anyone’s guess.

The race has been upended by the late entry of Eric Hovde, 48, a banker, investor and hedge-fund manager who had not lived in the state for 24 years until moving back from Washington, D.C., in 2011. Although Thompson likes to point out that Hovde’s first vote for U.S. senator will be the one he casts for himself, the political newcomer has spent more than $4 million of his own money on advertising that portrays him as a fresh face with business expertise.

That created a possible opening for former congressman Mark Neumann, who also has benefited from the backing of national conservative leaders and from $700,000 in attack ads against Thompson and Hovde by the conservative group Club for Growth.

The anti-tax organization is hoping for a repeat of what happened this week in Texas, where the group’s ads were a significant factor in the GOP primary victory of Ted Cruz over the better-known, better-funded longtime Lt. Gov. David Dewhurst.

“It’s been tough. I’ve been outspent 10 to one, mostly with negative ads,” Thompson said in an interview Wednesday. “But I’m still standing, and I'm still leading.”

That is debatable. Polling over the past few weeks has shown that what was once an expected coronation has turned into a free-for-all, with a large portion of voters remaining undecided. A survey released Tuesday by the Democratic firm Public Policy Polling found that the three leading contenders are virtually tied.

Although PPP uses an automated technique that many other pollsters do not regard as reliable, its result underscores a trend that other political analysts are sensing as well.

“I find it credible and plausible” that the race is now a dead heat, said Charles Franklin, a political scientist at Marquette University Law School in Milwaukee who runs a polling operation and will be going into the field this week.

In July, Marquette’s polling showed Thompson with a double-digit lead, although it found evidence that Hovde was gaining ground.

That was largely the result of the fact that his advertising had been on the air for weeks, with no response from the Thompson or Neumann camps.

“It’s a strange thing for an old pro like Thompson to give anyone an uncontested platform for such a length of time,” Franklin said.

Asked why, Thompson said he had not put up his own ads because he did not have the money to do so.

The Senate race had simmered on the back burner until recently, because Wisconsin voters had been riveted by — and then exhausted by — Republican Gov. Scott Walker’s successful effort to hold onto his job in a June recall election.

It remains a question how many and which Wisconsinites will even vote in the Aug. 14 primary. The state normally holds its primary in September, and has not had one in August since the World War II era.

“The date they picked is horrendous,” Thompson said. “It happens to be the week before the kids go back to school.” And after an intense round of recall elections arising from Walker and the Republican legislature’s move to limit collective bargaining for public employees, “people are tired of giving and are tired of politics,” Thompson said.

Assembly Speaker Jeff Fitzgerald, who is running a distant fourth behind his better-funded competitors, agreed. “The governor and state Senate recalls really kind of soaked up the dollars,” he said. “It’s been tough to get volunteers. It has been tough to get anybody excited again.”

Although the assumption by all the campaigns is that the primary will be dominated by die-hard conservatives, Wisconsin does not register voters by party, which means that even Democrats can vote for a Republican. Franklin said he expects about one in 10 of the primary voters to be Democrats.

All three candidates have tried to position themselves as the natural beneficiaries of the movement that grew up around Walker’s June victory in the recall election.

Even Neumann, who ran against Walker for the GOP gubernatorial nomination in 2010, is basking in the governor’s glow.

“The identity of the Republican Party was well defined by Scott Walker and his team,” he said in an interview. “We do not have to settle. Folks are committed and understand we are the true conservative in the race.”

Hovde declined a request for an interview.

Meanwhile, Walker has expressed some dismay about the nasty turn the race has taken in recent weeks.

Rather than supporting a candidate, he had said he will stand on the sidelines as a referee, guarding against any of the contenders crossing the line. “I haven’t dropped a flag yet, but it’s getting pretty close,” he said Tuesday at a news conference.

The fear among Republicans is that their candidates will do so much damage to one another that whoever manages to limp away from the primary contest will start at a significant disadvantage to Rep. Tammy Baldwin, who is the only candidate vying for the Democratic nomination.

At 70, Thompson maintains an enthusiasm for the retail side of politics that appears undiminished. He boasts that the blistering weather did not deter him from marching in four parades on the Fourth of July. “Not just walking,” he said. “I ran back and forth shaking hands in 103-degree heat on blacktop.”

On Wednesday, as he toured Sadoff Iron & Metal, an enormous scrap-metal facility here, the former governor — wearing a hard hat, safety glasses and a neon vest — tried not to miss a single potential voter. At one point, he climbed up to the cab of a crane to talk to the operator. Then, ducking into administrative offices, he called out: “Remember now, Tommy Thompson on the 14th.”

Management trainee Steve Crowley, 33, recalled meeting Thompson once before — as a 9-year-old Cub Scout on a visit to the state capital.

Said Thompson: “Eighty-eight percent of the people know me as ‘Tommy’ in the state, which is pretty darn nice.”

However much affection the state has retained for Thompson since he left more than a decade ago to become president George W. Bush’s health and human services secretary and then to join a lobbying and law firm in Washington, his opponents suggest that the former governor’s time has passed, and that his amiable brand of politics is insufficiently conservative for the tea party era of Republican politics.

What Hovde lacks in political experience he more than makes up for in self-confidence. He has even gone so far as to suggest that Thompson does not have the intellectual heft needed for the job.

“I think these are issues I can talk about that, quite frankly, Tommy Thompson would have a hard time understanding,” Hovde said last month.

To which Thompson retorted: “I would say anybody that makes those kind of statements is not very bright.”