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A state known for its racially charged politics may be on the cusp of nominating an Indian-American woman for governor and a black man for U.S. representative.
Both candidates advanced to runoffs with their top challengers after the state primary elections two weeks ago.
Elsewhere, several high-stake runoffs are being held in North Carolina, Mississippi and Utah.
The gubernatorial race in South Carolina has been closely watched. The GOP primary was marked by what Haley has described as "dirty politics," as first a blogger and then a lobbyist claimed they had affairs with the candidate, which she denied. A state senator called Haley a "raghead" and the final stretch of the race saw questions about her Christian faith -- Haley was raised Sikh by Indian-American parents.
Despite the drama, Haley emerged relatively unscathed in the primary, winning 49 percent of the vote against three established Republican competitors. U.S. Rep. Gresham Barrett, who came in a distant second with 22 percent, advanced to the runoff.
Haley told Fox News that the willingness of voters to accept her candidacy shows the state is moving beyond wanting to hear "dirt about the other opponents."
"They now want to talk about issues that affect wallets and affect their businesses every day," she said. "They want to hear about what that candidate is going to do for them."
The race also signaled a potential shift toward more diversity among South Carolina's elected officials. If she wins, Haley would move a big step closer to being the state's first female governor and one of a handful of Indian-Americans in top elected positions.
Scott, who is going up against Paul Thurmond -- son of the late U.S. senator and former segregationist Strom Thurmond -- has a good shot at being the first black GOP congressman for his state in more than a century. Also, a black Republican has not held a seat in Congress since Oklahoma Rep. J.C. Watts left in 2003.
Scott is favored to win against Thurmond. He won 31 percent of the primary vote in a nine-way primary, with Thurmond a distant second.
Six-term Rep. Bob Inglis is also struggling to hold on to his House seat in a GOP runoff against prosecutor Trey Gowdy.
The Senate contest in Utah is less predictable. Illustrating how fractured the Tea Party movement is, one of the founders of the state's movement, David Kirkham, endorsed front-runner Tim Bridgewater on Monday. But attorney Mike Lee, 38, had already picked up the support of the California-based Tea Party Express, which is weighing in on primary races nationwide.
The two candidates advanced after U.S. Sen. Bob Bennett was ousted at the GOP state convention.
Bridgewater and Lee moved forward on promises to rein in federal spending. But without an incumbent in the race and little to distinguish their platforms, Tea Party supporters have struggled to coalesce around a single candidate.
A lot is at stake. Whoever wins Tuesday's GOP nomination should cruise to victory in November in heavily Republican Utah. A Democrat hasn't won a U.S. Senate race here since 1970.
In North Carolina, Secretary of State Elaine Marshall is locked in a close runoff against Cal Cunningham, the favorite of Democratic Party leaders in Washington, for the party nod for the Senate. The winner faces an uphill race against Republican Sen. Richard Burr.
Mississippi also has a runoff for the Republican nominee in a House race.
Also on Tuesday, Democrats will choose their nominee in Utah's 2nd Congressional District. U.S. Rep. Jim Matheson is seeking a sixth term, but is facing a challenge from his left by retired teacher Claudia Wright.
Wright won 45 percent of the vote at the Democratic convention, forcing Matheson into his first-ever Democratic primary. Matheson is being targeted by the left for voting against President Obama's health care bill. Matheson has since said he would oppose repealing the legislation.
The Associated Press contributed to this report.