(Columbia-AP) June 23, 2004 - Fourth District Congressman Jim DeMint overcame relative obscurity statewide and overwhelmingly beat former Governor David Beasley in the Republican runoff for US Senate. SC Votes '04 runoff election returns>>

DeMint told supporters Tuesday evening, "Folks, mission two accomplished, we're in the finals now." Voters who returned to the polls Tuesday picked DeMint 59 percent to 41 percent over Beasley in unofficial results with 100 percent of precincts reporting.

The three-term congressman from Greenville, says he has specific solutions for the problems the state is facing. DeMint told The Associated Press that voters selected him because he has specific solutions for the problems the state is facing.

DeMint knows he has another tough campaign, "The Republican Party all over the country is looking at this race. And, I know I have asked a lot of you for help, but we're going to go the extra mile and win this race in November. It's going to be the best victory we've ever had in the state. And I forgot something, the President just called, too."

DeMint will now face Democratic state Education Superintendent Inez Tenenbaum this fall to replace retiring Senator Ernest Hollings. The Democrat has held his seat for nearly 40 years.

DeMint refused to discuss what strategy he might use in November when he faces Tenenbaum, but his campaign spokeswoman Kara Borie called Tenenbaum a formidable opponent. She says it's important that the Republican Party unites.

Tenenbaum says she called DeMint to congratulate him and called Beasley to commend him.

Beasley and DeMint had been in a fierce battle since they emerged from the six-way June 8th primary as the top vote-getters. Beasley actually finished that race with the most votes, but since neither got more than 50 percent, a runoff was scheduled.

Beasley says his campaign fought hard and did what was good and right, but he pulled no punches about his defeat, "We got whipped tonight, that's no exaggeration." Beasley thanked his campaign during a speech at a Columbia hotel. He says all that his campaign stood for is bigger than Jim DeMint and David Beasley.

The former governor was apparently unable to shake his past. He was questioned about differing opinions and exaggerations on things such as athletic feats and the amount opponents spent to beat him during his re-election bid six years ago.

He was ousted from the governor's office in 1998 after one term during which he changed his mind about the Confederate flag and called for its removal from atop the Statehouse.

He also did not rule out another run for office, "I can assure you that when that sun comes up tomorrow that David Beasley will not fade into the sunset. I'll rise again, fighting for what's good for South Carolina."

Beasley says DeMint is a good conservative Republican and the two candidates agree on almost all issues. He says they had a little disagreement on trade, but the two have agreed to sit down and talk about what's good for South Carolina.

The Upstate congressman spent $3.5 million and campaigned countless hours for a chance to replace the retiring Hollings, who has held his seat for nearly 40 years.

DeMint did very well in the Lowcountry, which was expected to be the battleground in the race. He won Berkeley and Dorchester Counties by a two-to-one margin and he won Charleston County three-to-one.

Two weeks ago, DeMint trailed Beasley in all three counties before he got a key endorsement from Thomas Ravenel, the Charleston businessman who just missed knocking DeMint out of the runoff. Former Attorney General Charlie Condon also finished behind Beasley and DeMint, but eventually endorsed DeMint.

Tenenbaum has piled up huge numbers in winning the superintendent's job twice. She has already begun working to try and keep Republicans from painting her as a liberal Democrat. For instance, she favors the death penalty and a ban on some late term abortions.

The big issue in this race, like the primary, will be trade and jobs. DeMint favors free trade. Tenenbaum says she will vote against any trade treaty that costs South Carolina jobs and she wants to get tough on China.

DeMint says he may take a day or two off, but Tenenbaum begins her campaign Wednesday with a visit to a senior citizens center in Columbia.

Turnout was described as light throughout most of the state, but Republican Party officials predicted about 250,000 voters would return to the polls statewide. Almost 295,000 voted in the GOP Senate primary on June 8th. There were also several runoffs for General Assembly seats.

updated 7:47pm by BrettWitt with AP