Los Angeles ? How angry are Americans?

People primed for change vote in 12 states Tuesday in contests that will decide the fate of two endangered Washington incumbents — a two-term senator in Arkansas and a six-term congressman in South Carolina — while setting the stage for some of the races that could determine the balance of power on Capitol Hill in the fall.

In an Arkansas runoff, Sen. Blanche Lincoln could fall to a fellow Democrat, Lt. Gov. Bill Halter, who says “the only way to change Washington is to change who we send there.” South Carolina Republican Rep. Bob Inglis is trying to fend off primary challengers who have made the race a referendum on his 2008 vote to bail out up the nation’s banking industry.

The political strength of the tea party movement faces tests in several states, particularly in Nevada, where three Republicans are in a bruising fight for the chance to take on Democrat Harry Reid, the Senate majority leader, in November.

Republicans in California could send two political neophytes, wealthy former business executives Meg Whitman and Carly Fiorina, into races to succeed Gov. Arnold Schwarzenegger and challenge Democratic Sen. Barbara Boxer.

In an election season overshadowed by the ailing economy and unhappiness with Washington, three longtime incumbents already have lost: Sens. Bob Bennett, R-Utah, and Arlen Specter, D-Pa., and Rep. Alan Mollohan, D-W.Va. A party switcher new on the scene, Democrat-turned-Republican Rep. Parker Griffith of Alabama, stumbled this past week as voters demanded ideological purity.

Losing confidence

A Pew Research Center poll in April found that public confidence in government was at one of the lowest points in a half century. Bennett calls the political atmosphere toxic. Races on Tuesday will provide fresh evidence of how far people want to go to shake up statehouses and Washington.

“I’ve become frightened over what our government is doing,” says Roxanne Blum, 57, a Republican from Pahrump, Nev. She’s alarmed by the soaring debt and has seen firsthand, through her work in the mortgage industry, the damage caused by Nevada’s highest-in-the country foreclosure rate.

Once excited by Reid’s ascendancy in Washington leadership, she now sees him as out of touch with his economically troubled home state. “When he comes here, he does lip service,” she says.

Earlier congressional contests have shown that incumbency can be a yoke and that voter discontent is running through both parties, even though the Democrats who control Congress have the most at risk in November. With President Barack Obama’s popularity slipping, issues from the health care overhaul law to taxes are defining races.

Tea party-backed Mike Lee, one of two Republicans who advanced to a June 22 primary for Bennett’s Utah seat, says there’s “a widespread feeling the federal government is growing, taxing, spending and borrowing way too much.”

In the Arkansas runoff, Lincoln is suffering blowback from the right and left for her health care votes. Unions backing her rival have spent more than $5 million to defeat her. In one ad, she acknowledges the frustration among voters: “I know you’re angry at Washington.”

California race

The Republican race to succeed Schwarzenegger has been a display of extraordinary spending as well as a test of how far right the party wants to venture on issues such as illegal immigration in a traditionally Democratic-tilting state.

Republican billionaire Whitman, a former eBay chief executive, has invested more than $70 million of her own fortune in the race against state insurance commissioner Steve Poizner, a wealthy former businessman who has put $24 million into his campaign. The all-but-certain Democratic nominee is Attorney General Jerry Brown, who was governor in the 1970s and 1980s.

Whitman and Poizner have challenged each other’s conservative credentials in a torrent of negative ads. Poizner supports Arizona’s tough illegal immigration law; Whitman does not. Poizner wants to cut off most state services to illegal immigrants and their children; Whitman would not end services for children.

In a year of tea party insurgency, “all of the Republican candidates in California have been pulled to the right,” says political scientist Bruce Cain of the University of California, Berkeley. The question in November will be whether independents who cast decisive votes follow.

Fiorina, a former Hewlett Packard Co. chief executive who has Sarah Palin’s endorsement, has a lead in polls over former U.S. Rep. Tom Campbell and state Assemblyman Chuck DeVore, a tea party favorite. Boxer’s campaign has depicted the Republicans as out of step with mainstream Californians.