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Mr. Johnson won that way over incumbent Sen. Russ Feingold in 2010 in Wisconsin, as Sen. Mike Lee of Utah did in his Republican primary victory over incumbent Sen. Robert F. Bennett that year. This year, Republican Sen. Richard G. Lugar of Indiana was toppled in his primary by tea party candidate Richard Mourdock.

While precedent may be on Mr. Hovde’s side, it won’t be nearly as easy for him to portray Mr. Thompson — who has not held elected office in 11 years — as complicit with the gridlock in Congress, said Eric Ostermeier, a political analyst at the University of Minnesota.

Other frontrunners “were running against not only an insurgent candidate but had to defend themselves as being part of the problem,” Mr. Ostermeier said. “Thompson’s a little insulated from that.”

There are other factors that could tip the primary in Mr. Thompson’s favor, such as lasting positive name recognition from his time as governor and the fact that an open primary could allow moderate Democrats to abandon their party’s uncontested primary.

But Jennifer Duffy, an analyst for Cook Political Report, suggested there may be voter fatigue in the state after a string of recall elections, which could depress voter turnout among moderate or apathetic voters — providing a likely advantage for Mr. Hovde.

Nonetheless, she said Mr. Hovde has an uphill battle.

“We’re going to have to see, but I don’t think that Thompson is in a particularly terrible position,” she said.