South Carolina Democratic U.S. Senate candidate Inez Tenenbaum (search) accused Republican opponent Rep. Jim DeMint (search) of patronizing her by saying she doesn't understand key national issues during a fiery televised debate Sunday.

The two candidates challenged each other's positions on everything from Social Security and taxes to national security and abortion during the debate at the College of Charleston.

"I don't want to get her started again, but I'm afraid she really doesn't understand how Social Security is set up," DeMint said.

"Jim's only response to anything I say is: 'She doesn't understand,'" said Tenenbaum, the state education superintendent. "Frankly, Jim, that's a little patronizing. And really, you've got daughters of your own. You really ought to not do that anymore."

DeMint apologized, but soon made a similar statement while he defended calling Tenenbaum a "nice lady" on the campaign trail and in radio ads.

"I won't make that mistake again because I no longer believe it," DeMint said. "I'm sorry I called her a nice lady," he said. But "the fact is she doesn't understand a lot of the things she is talking about," DeMint said.

The pair were questioned about a state Republican Party platform item that says gays should not teach in public schools.

"I don't think they should," DeMint said. "We need the folks that are teaching in schools to represent our values."

"To say that a homosexual can't teach in a public school is really a bad thing and it's just un-American," Tenenbaum said.

Tenenbaum criticized DeMint's support of a plan to implement a national sales tax, which she said would hurt the economy and raise the cost of everything from drugs to gasoline while eliminating perks in the current tax code, including the home mortgage interest deduction.

DeMint he wants to eliminate the U.S. tax code because it costs jobs by making the nation less attractive for businesses. He added that people would be able to pay a national sales tax because they would no longer have taxes withheld from their paychecks.

The candidate, running Nov. 2 to replace retiring Democratic Sen. Ernest "Fritz" Hollings, have five other debates scheduled this month, including one on NBC's "Meet the Press" on Oct. 17.