Speaking to an enthusiastic crowd of about 300 in Rock Hill, the former House speaker also pledged to fight "anti-Christian bigotry."
Gingrich has had disappointing finishes in Iowa and New Hampshire but made clear Wednesday that he isn't going down without a fight.
South Carolina's Jan. 21 primary is the first in the South and critical for the Georgia congressman. Gingrich hopes to appeal to the state's evangelical and socially conservative voters, some of whom are skeptical of Mitt Romney, the GOP front-runner.
Gingrich played up his regional ties, saying "It's good to be home in the South."
Gingrich finished well behind the leaders in Tuesday's New Hampshire Republican primary, tying for fourth place with Rick Santorum.
"We're going to offer the American people something very different," Gingrich told about 200 supporters at a downtown Manchester, N.H. hotel. "We're going to offer them the opportunity to participate in very dramatic, very fundamental change in Washington."
Later in his speech, the former House speaker urged those in the New Hampshire crowd to call everyone they know in South Carolina and Florida and get them to come aboard.
Gingrich fell behind Mitt Romney, Ron Paul and Jon Huntsman in the contest. He was locked in a tight battle with Rick Santorum for fourth place.
"This is step two of a long process," Gingrich said. "We have an opportunity, I think, to unify the country around a message of jobs, economic growth and very dramatic change,"
The first Southern primary, on Jan. 21 in South Carolina, is critical for the former Georgia congressman. And the race there promises to be bruising.
Gingrich has already put up ads in South Carolina attacking Romney for his "timid" economic proposal and hitting him for shifting views on abortion. "Massachusetts moderate Mitt Romney," the spot intones. "He can't be trusted."
And a pro-Gingrich PAC has snapped up $3.4 million in airtime and is expected to saturate the airwaves with ads taking aim at Romney's leadership at Bain Capital. Winning Our Future has assembled a 28-minute video which assails Romney for "reaping massive awards" while head of the venture capital firm.
Gingrich, 68, began his White House bid in Iowa pledging to run a positive campaign. But after being battered by a deluge of ads _ most funded by pro-Romney PAC _ Gingrich shifted gears and began to hit back hard.
Gingrich has said the race is about contrasts and has sought to cast himself as the bold conservative heir to the mantle of Ronald Reagan. And he argues that although Romney has now racked up back-to-back wins in Iowa and New Hampshire, he has done so with below the majority of the voters, meaning that most of the GOP's conservatives are voting against Romney.
South Carolina, Gingrich said, won't take kindly to a moderate from the state that brought the nation Democrats John Kerry and Michael Dukakis.
"The ideal South Carolina fight would be a Georgia conservative vs. a Massachussetts moderate," Gingrich told reporters Tuesday.