WASHINGTON -- Tommy Thompson beat three other Republicans for the party's U.S. Senate nomination in Wisconsin on Tuesday night, allowing him to challenge Rep. Tammy Baldwin (D-Wis.) in November for an open seat.

In his victory speech, Thompson acknowledged the "hard-fought campaign" and encouraged supporters to get fired up for November -- not only for his race, but also for the presidential contest. He predicted Republicans would send President Barack Obama "back to Chicago" to "be a community organizer again."

The Senate race between Thompson and Baldwin is likely to be tight. A recent Quinnipiac survey showed the two tied. The winner succeeds retiring Democratic Sen. Herb Kohl.

Thompson, 70, the former governor of Wisconsin and the Health and Human Services secretary under ex-President George W. Bush, initially was considered the frontrunner in Tuesday's GOP primary because of his long career in public service and popularity in the state. But businessman Eric Hovde surged in recent weeks, using his personal fortune.

Former congressman Mark Neumann -- who had the support of conservatives who include Sen. Jim DeMint (R-S.C.) and the Club for Growth -- was close behind, making it a three-way contest. He, like Hovde, tried to capture voters who worried that Thompson is too moderate. Wisconsin Assembly Speaker Jeff Fitzgerald lagged in the polls and fundraising.

Fitzgerald dropped out early on Tuesday night, followed by Neumann, who endorsed Thompson in his concession speech.

Thompson received a boost from a mention by Rep. Paul Ryan (R-Wis.) on Sunday, when Ryan was in Waukesha for a rally after being named as Mitt Romney's running mate the day before. Ryan did not endorse anyone in the race, but gave Thompson a shout-out, which Thompson's campaign touted in the following days.

Baldwin, 50, a veteran member of congress, faced no primary opposition. Democrats and progressive groups on Tuesday were already preparing efforts to help Baldwin, with a fuller effort set to launch on Wednesday.

Former Wisconsin senator Russ Feingold will jump into the race on Wednesday to help Baldwin. His Progressives United group, along with a handful of other progressive organizations and individuals, will begin a "Cheddarbomb" fundraising drive.

Feingold told The Huffington Post he was confident Baldwin could beat Thompson.

"Tommy has regularly made it his business to mock the United States Senate, saying things like, why would you want to be one of 100, when he was governor of Wisconsin," Feingold said. "It almost seems like he's doing this because he's looking for something to do.

"It doesn't seem like he's been very focused on wanting to be a member of the United States Senate. Representing Wisconsin to the Senate is sort of his latest gig after he ran for president, whereas Tammy Baldwin has made a serious career out of trying to be a legislator at the national level. The contrast between the two is clear," Feingold added.

The Cheddarbomb fund drive that Feingold helped lead in 2010, when he was running for reelection as senator, brought in more than $435,971 in one day.

"We did the original Cheddarbomb in our campaign," Feingold said. "It was probably the biggest success in terms of raising small dollars from a lot of average folks of everything we did. It's just an example of the kind of fundraising that should dominate the political process, instead of the post-Citizens United unlimited undisclosed contributions. This is the polar opposite, in the most democratic way to do it."

The AFL-CIO super PAC Workers' Voice began running an online ad in support of Baldwin on Wednesday morning. Visitors to the website of the Milwaukee Journal Sentinel will see a large AFL-CIO ad that will direct them to a site about Baldwin.

And on Tuesday morning, the pro-lesbian super PAC known as LPAC threw its support behind Baldwin, in its first endorsement of the 2012 cycle.

Even before polls closed on Tuesday, Baldwin challenged her future GOP challenger to three general election debates.

Turnout had been expected to be low on Tuesday. Election officials predicted about 20 percent of registered voters would show. WisPolitics noted on Tuesday afternoon that the city of Milwaukee ratcheted down projections to 18 percent to 20 percent, from its earlier projection of 20 percent to 25 percent. Associated Press reporter Scott Bauer reported on Twitter that he encountered "lots of anger, fatigue among voters at the polls today in Madison." Wisconsinites, after all, have now had five elections since February, including the high-profile recall election of the governor, lieutenant governor and several state senators.

UPDATE: 12:24 a.m. -- This article has been updated to include Thompson's comments in his victory speech.

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