Newt Gingrich turned his rhetorical guns on U.S. President Barack Obama and the "elites" in Washington and the American media following his victory in South Carolina on Saturday night.

Newt Gingrich, flanked by his wife Callista, slammed U.S. President Barack Obama in his victory speech in Columbia, S.C., on Saturday night. Jason Reed/ReutersSpeaking to wildly enthusiastic supporters in Columbus, the former House speaker offered warm words to the rivals he defeated — even Mitt Romney, whom he slammed earlier in the week as a job killer — calling them examples of how people from every walk of life in the United States can make their voices heard on the national stage.

But he quickly refocused his comments on Obama, calling him "a president so weak he makes [former Democratic U.S. president] Jimmy Carter look strong."

Obama is "the most effective food stamp president in history," he said. "I would like to be the best paycheque president in American history."

Those declarations and his attack on the "elite news media" reprised two of his more memorable lines from a pair of debates that helped fuel his victory.

He slammed the Obama administration's recent decision to shelve TransCanada's Keystone XL pipeline, a project he erroneously said would bring much-needed oil to Texas from "central Canada."

Prime Minister Stephen Harper is a "conservative and a pro-American," Gingrich said, and now Canada will be forced to sell its oil to China.

"An American president who can create a Chinese-Canadian partnership is truly a danger to this country," he said.

"It's one thing to not be able to play chess, it's another not to be able to play checkers. But when you can't play tic-tac-toe …," Gingrich said to laughter and cheers from the crowd.

"We don't have the kind of money that at least one of the candidates has," he said in a reference to Romney. "And we proved here in South Carolina that people powered with the right ideas beats big money."

Romney launches veiled attack on Gingrich

Mitt Romney, the national front-runner until Saturday's stunning double-digit defeat in South Carolina, vowed to contest for every vote "in every state," an acknowledgement that the race would likely be a long one. The former Massachusetts governor also unleashed a veiled attack on Gingrich.

"When my opponents attack success and free enterprise, they're not only attacking me, they're attacking every person who dreams of a better future. He's attacking you," he told supporters in Columbia, the state capital. It was the closest he came to mentioning Gingrich's name in his speech.

"I don't shrink from competition," he said. "We're going to win this nomination and we're going to beat President Obama in November."

Santorum bloodied but unbowed

Rick Santorum gives a thumbs up as he leaves the stage at the end of his South Carolina primary night rally in Charleston, S.C. Randall Hill/ReutersRick Santorum cast his disappointing third-place finish in this state's primary as a hiccup and pledged Saturday to continue with a campaign that he called "wide open."

"Let me assure you we will go to Florida and we will go to Arizona," the former Pennsylvania senator said before supporters interrupted him with chants of "We pick Rick."

"I ask you: It's a wide-open race — join the fight," Santorum urged the crowd at an election night rally at the Citadel, a South Carolina military college. "Three states. Three different winners. What a great country."

Santorum's outside allies seemed poised to bankroll supportive ads, at least for now.

"The longer we can keep his candidacy going, the more people can see his qualities," said Foster Friess, a Wyoming businessman and a major contributor to the Red, White and Blue Fund, a SuperPAC supporting Santorum. "If you look at Republicans, they always run these old war horses. Santorum is different."

Paul won't give up fight

Ron Paul tells his supporters he will continue to battle for the Republican presidential nomination during a speech in Columbia, S.C. on Saturday night.Benjamin Myers/ReutersRon Paul, who had his worst finish of the year and isn't expected to make a strong effort in Florida, urged his supporters to "keep fighting," adding he intends to largely skip Florida, which holds its primary Jan. 31, and focus his efforts on caucus contests in Nevada on Feb. 4 and Missouri several days later.

"This is the beginning of a long, hard job," the Texas congressman told fans gathered at a sports bar in Columbia, the state capital. "We want a free society and a prosperous society, and we are on the verge of a victory for those issues today.

"Ever notice how the other candidates go up and then down? I am proud of our efforts at steady growth," Paul told supporters. The group cheered, yelling "President Paul! President Paul!"

Paul's libertarian message found some traction in South Carolina, but his call to vastly cut military spending hit a stone wall in a state that's home to many military bases and veterans.

With files from The Associated Press