Many fiscal conservatives don't like Thompson because of his record on taxes, spending and healthcare — but if Hovde and Neumann both remain credible candidates they could split the anti-Thompson vote, improving the former governor's chances in the race.

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Hovde, a wealthy businessman, has been spending heavily to boost his name recognition in the state, and recent polls show him leapfrogging Neumann and running competitively against Thompson.

But on Friday morning the deep-pocketed, fiscally conservative Club for Growth — which often is on the same side as FreedomWorks in races — began a major advertising campaign attacking both Hovde and Thompson for their tax views. Sen. Jim DeMint's (R-S.C.) Senate Conservatives Fund is also backing Neumann.

Some conservatives in the state remain unhappy with Neumann for his testy 2010 primary against Wisconsin Gov. Scott Walker (R), a reason Pappas mentioned to The Hill in late June for why the group would be unlikely to back him in the primary.

The three, and Wisconsin State Assembly Speaker Jeff Fitzgerald (R), are vying to face Rep. Tammy BaldwinTammy BaldwinOvernight Regulation: Labor groups fear rollback of Obama worker protection rule | Trump regs czar advances in Senate | New FCC enforcement chief Dems urge Sessions to reject AT&T-Time Warner merger In Wisconsin, Trump touts 'earn while you learn' jobs push MORE (D-Wis.) in the fall.

The Hill rates this race a toss-up, though Republicans likely have the best shot at winning the seat if Thompson is the nominee.