Linda McMahon, who lost a bid for a Connecticut Senate seat in 2010, will make another try in 2012 after easily winning a primary contest against moderate former House member Chris Shays.

In defeating Christopher Shays, a former United States representative and longtime fixture in moderate politics in the state, Ms. McMahon underscored the power of being an outside candidate, as well as a wealthy one. She outspent her opponent nearly 12 to 1, and flooded the airwaves with advertisements promoting herself as a political maverick who could bring common sense to Washington.

It appeared that Mr. Shays, who held his House seat for two decades before losing his bid to keep it in 2008, was tripped up by the Washington experience and centrist viewpoints that once made him one of the more popular Republicans in a left-leaning state.

Before a roaring crowd in Stamford, Ms. McMahon took the stage hours after her win and told supporters that she would jump-start a stagnant economy. "We need to give all these career politicians in Washington who have agreed to this mess a pink slip!" she said.

Mr. Shays met reporters at his sparse campaign headquarters and said he would support his opponent in the general election. Ms. McMahon's millions, he added, "trumped the experience we bring to the table."

Ms. McMahon will face Representative Christopher S. Murphy, a Democrat, in the November election for the seat being vacated by Senator Joseph I. Lieberman, an Independent. Mr. Murphy won his primary on Tuesday, by a wide margin over his opponent, Susan Bysiewicz, a former secretary of the state.

McMahon can draw on a massive personal fortune to augment her considerable war chest. But she spent $50 million in 2010 and lost by 11 points. Connecticut might be the second most Democratic state in the union behind Massachusetts and it will be an uphill battle for her to win.

Meanwhile, in Wisconsin, former Governor Tommy Thompson won his primary over two, more conservative opponents.

With 82 percent of precincts reporting, Thompson led a four-way field with 35 percent of the vote, followed by businessman Eric Hovde (R) at 30 percent, former Rep. Mark Neumann (R-Wis.) at 23 percent and Wisconsin Assembly Speaker Jeff Fitzgerald at 12 percent. The Associated Press has called the race.

Thompson will face Rep. Tammy Baldwin (D-Wis.), who was uncontested in her primary. Polls show the race will be competitive in the slightly Democratic-leaning state: In the last three public polls of the race, Thompson leads in one, Baldwin leads in another and they are tied in the third. Thompson likely starts the race with a slight edge due to his popularity with independents in the state, though Baldwin has the cash advantage at this point.

Democrats have said they'll hit Thompson on his years in Washington, D.C. following his time working as President George W. Bush's secretary of Health and Human Services, which he spent working as a consultant for a number of health insurance groups. Republicans have promise to make Baldwin's strongly liberal record a top target, especially her support of a single-payer, government-run healthcare system.

The choice of Paul Ryan will be a plus for Thompson who needs a large turnout of conservatives and independents to overcome the registration advantage of Democrats in the state. Still, the GOP has won the last 3 statewide races, including the recall election of Governor Walker last spring.

As for McMahon, it might depend on the depth of anti-incumbent, anti-Washington sentiment in the state. If she can make Murphy into the Washington insider she portrayed Shays, she will have a fighting chance in November.