(CNN) -- Sen. Barack Obama sought Sunday to use his South Carolina victory to expand his appeal, saying the first Southern primary reflects what Americans are looking for.
Hillary Clinton, from left, John Edwards and Barack Obama have different takes on the primary message.
Speaking to ABC's "This Week," Obama argued that the result in South Carolina "speaks extraordinarily well, not just for folks in the South, but all across the country. I think people want change."
But Sen. Hillary Clinton noted that both she and her top Democratic rival "have won a primary and a caucus."
And she told CBS' "Face the Nation" that the election ultimately is not about the candidates, but "about what we're going to do as a country and the lives of the people watching us."
Clinton also suggested that the dynamic in the tightly contested race for the Democratic presidential nomination could shift again in two days when Florida holds its primary.
"I'll be there Tuesday night," Clinton said. Watch how Clinton is fighting on despite the setback »
Florida's delegates are not slotted to count in the race, and the Democratic candidates opted not to campaign there, steps called for by the Democratic Party as a way of penalizing the state for moving its primary to an earlier date.
Many Florida Democrats have complained they want their votes counted, and Clinton has called on the party to seat delegates from Florida and Michigan -- which was similarly penalized -- at the party convention this summer.
Both Clinton and Obama -- as well as former Sen. John Edwards, who has not won any of the early states -- are pouring their energy and money into Super Tuesday, the biggest single-day showdown of the race. Nearly two dozen states will weigh in February 5.
While the former North Carolina senator had hoped to make a strong showing in his native South Carolina, he insisted he was not disappointed. "We were very encouraged about what happened," he told CNN Saturday. Watch Edwards try to rally supporters after South Carolina defeat »
He added that "in the last couple of weeks, we've had extraordinary online contributions" and vowed that he will become president.
"I still believe very strongly that I'm the strongest general election candidate," he said.
By routing his competitors Saturday in South Carolina, Obama pulled even in the early-state race with Clinton -- they each have won two states -- and claimed his first victory since the Iowa caucuses earlier this month.
Obama won South Carolina with the help of a large majority of the state's African-American voters. The majority of white voters in the primary supported his rivals, exit polls showed.
A question facing his campaign is whether he can expand his demographic reach in states throughout the country.
Speaking Sunday to ABC during a campaign stop in Macon, Georgia, Obama said South Carolina voters showed they "want to get beyond some of the racial politics that, you know, has been so dominant in the past. We're very encouraged as we go to the February 5 states." See scenes from polling places across South Carolina »
But Clinton, on CBS, said, "We've got a long way to go" in the race toward the nomination. She said she would continue focusing on critical issues such as "whether or not the economy works and health care is there, and, you know, all of the big challenges and opportunities we face."
Speaking from a campaign stop in Memphis, Tennessee, she added, "I wake up every morning and I think about what I'm going to do today, what kind of a difference I'm going to make in people's lives."
Democratic candidates will debate the issues on CNN at 8 p.m. Thursday in their final meeting before the Super Tuesday primaries. The Republican candidates will debate on Wednesday.
Both Clinton and Obama suggested they're prepared to shelve some of the bickering of recent days to improve the tone of the campaign.
Clinton said even the media shared this responsibility "because I think that we stand for so much bigger than, you know, what divides us. And we've got to make that case."
Obama told ABC, "What I want to do is try as much as possible to spend the remaining weeks and potentially months of the campaign talking about the issues that all Democrats should be concerned about, and I think all Americans should be concerned about." Watch what the South Carolina win means to the Obama camp »
"My suspicion is that by the time we get a Democratic nominee, the party will be unified and it will be energized," he added.
On that point, Clinton agreed: "At the end of the day, we will come together as Democrats. We will be a united and committed party to take back the White House in November." E-mail to a friend