George Bush took the Republican presidential campaign into Jimmy Cater's southland today, declaring that Republicans "are the party of new idea for the '80s, while they [Democrats] are the party with the failed answers."

Moving smoothly into his "give-'em-hell-with-a-smile" role, Ronald Reagan's vice presidential nominee spent the day, his official campaign kickoff, in South Carolina, attacking what he called the failures of Carter's economic policies in an attempt to lure the conservative working-class Democrats into a Republican way of thinking.

"I believe that the unemployment figures, which are really ripping off families, the inflation figures that are doing the same thing . . . all these things will come together and people in this state will say, 'I want a change,'" Bush said.

That optimism, however, is set against a bleak backdrop of recent Republican failures in this heavily Democratic state. While there is no party registration here in this spring's Republican primary, the state's first, only about one-tenth as many people voted as usually turn out for Democratic contests.

To win the state's eight electoral votes for the Reagan-Bush ticket, state GOP chairman George Graham said, "We've got to take away the blue-collar, working-class vote," which went overwhelmingly for Carter in 1976. He carried the state by 57 to 43 percent over then-President Ford.

But Bush spent little time today talking about numbers, preferring instead to hammer away at Carter's record and to bask in the warm reception given by Sen. Strom Thurmond, the state's leading Republican and one of its most popular politicians.

Thurmond welcomed Bush at the Florence airport, and took him before a crowd of 80,000 raucous stock car racing fans at the Darlington 500. The welcome for Bush was polite but not overwhelming -- but President Carter's son Chip, introduced immediately after Bush in an apparent snafu, received a smattering of boos.

Getting into the spirit of the boisterous, sun-and-alcohol-drenched fans, Bush moved along the infield rail, shaking hands and donning billed caps -- one for Purolator, one for Gatorade and one for STP.

After quickly rounding the track on the back of a convertible, Bush watched about an hour of the ear-shattering race, then appeared at a reception for Republican congressional candidate John Napier, who is challenging incumbent John W. Jenrette Jr., one of the congressmen indicted in the Abscam scandal. Bush later flew to Orlando, Fla., to continue his southern swing.