Los Angeles, California (CNN) -- A number of high-profile primary battles highlight races in 12 states Tuesday, including a senator trying to save her political life and a runoff in a special congressional election to fill a vacant House seat.
In California, a large state with pricey television markets, campaigning can be expensive. But that doesn't seem to be a problem for wealthy candidates Meg Whitman and Steve Poizner in the battle for the Republican gubernatorial nomination.
Whitman, the billionaire former eBay CEO who also was an adviser and surrogate for Sen. John McCain's 2008 presidential bid, has spent around $70 million of her own money. Poizner, California's insurance commissioner and a self-made multimillionaire, has injected some $25 million of his money into his campaign.
The most recent polls of likely GOP primary voters indicate that Whitman leads Poizner by around a 2-1 margin. The Republican winner in Tuesday's primary likely will face off in the general election against state Attorney General Jerry Brown, a former two-term governor and the presumptive Democratic nominee.
The winner in November will succeed Republican Gov. Arnold Schwarzenegger, who can't seek re-election because of term limits.
According to two surveys out this past week, former Hewlett Packard CEO Carly Fiorina is the front-runner in the battle for the Republican Senate nomination. Both polls indicate Fiorina leads former Rep. Tom Campbell by double digits. State Assemblyman Chuck DeVore, a conservative who is a favorite of Tea Party activists, is in third place.
The winner will face three-term Democratic Sen. Barbara Boxer in November. Polls suggest that Boxer faces a tough re-election battle.
The controversial new immigration law in neighboring Arizona has become a big issue in both the gubernatorial and Senate battles, as has the issue of offshore oil drilling due to the oil disaster in the Gulf of Mexico.
Arizona's immigration measure also is grabbing attention in Nevada, where 13 candidates are on the ballot in the Republican U.S. Senate primary. Two new surveys indicate that Sharron Angle is the front-runner. The former Nevada Assembly member, who praises the Tea Party movement, has won endorsements in recent months from many conservative organizations, including significant financial backing from the Tea Party Express, a national Tea Party group best known for running cross-country bus caravans, and the Club for Growth, a fiscally conservative organization.
According to the polls, Las Vegas businessman and former University of Nevada-Las Vegas basketball player Danny Tarkanian (son of that school's legendary basketball coach, Jerry Tarkanian) and businesswoman and former Nevada GOP Party Chairwoman Sue Lowden remain competitive.
Lowden, once the leader in surveys, appears to have suffered from a much-publicized gaffe when she suggested at a town-hall meeting in rural Nevada that people could barter for medical care, recalling that some even traded chickens for doctors' services in the old days. The comments fueled sarcasm and criticism of Lowden and her campaign.
The remaining candidates bidding for the Republican Senate nomination are in single digits in most polling.
The winner of the Republican primary will take on Senate Majority Leader Harry Reid, the presumptive Democratic nominee. Polls suggest Reid faces a tough bid for a fifth term in the Senate.
Two sitting senators, Republican Bob Bennett of Utah and Republican-turned-Democrat Arlen Specter of Pennsylvania, have been ousted so far this primary season. On Tuesday, Democratic Sen. Blanche Lincoln of Arkansas could become the third as she faces off in a Democratic primary runoff against state Lt. Gov. Bill Halter.
On Friday, Lincoln unveiled a campaign commercial featuring former President Clinton, an Arkansas native and longtime governor of the state. Clinton recently joined Lincoln at an event in Little Rock, too.
Halter has enjoyed the endorsement and financial support of national labor unions, which are targeting Lincoln for her opposition to the public option in the recent battle over health care (Lincoln voted for the final bill) and for her opposition to the Employee Free Choice Act, which unions strongly support.
Lincoln has fought back by portraying unions as Washington-based outsiders interfering in Arkansas politics. The runoff is necessary because while Lincoln edged Halter by 2 percentage points in the May 18 primary, neither candidate cracked the 50-percent mark needed for a victory.
The winner in Tuesday's runoff will face a tough general-election fight against Rep. John Boozman, the GOP nominee.
South Carolina's Republican gubernatorial contest is capturing national attention because of accusations of extramarital affairs.
The winner of Tuesday's contest hopes to succeed scandal-plagued Gov. Mark Sanford, a fellow Republican. A year after Sanford made national news for disappearing and then admitting to an affair with a woman from Argentina, allegations of infidelity now surround state lawmaker Nikki Haley, the leader in the most recent polls.
Haley has denied accusations of infidelity over the last two weeks, which she says rival campaigns are pushing.
To compound matters, a state lawmaker backing one of her rivals used a ethnic slur in describing both President Obama and Haley, who is of Sikh heritage. After an uproar by both state Republicans and Democrats, state Sen. Jake Knotts apologized.
Iowa, Maine, Montana, New Jersey, North Dakota, South Dakota and Virginia also are holding primaries Tuesday. There's also a runoff in Georgia to fill the seat of former Rep. Nathan Deal, a Republican who stepped down this year to run for governor. Both candidates in the runoff contest are Republicans.
CNN's Peter Hamby and Charles Riley contributed to this report.