Republican presidential candidates traveled through friendly territory Saturday, working to shore up support among key constituencies in an increasingly competitive and unpredictable nomination battle.

As former Massachusetts governor Mitt Romney spent the day in Salt Lake City celebrating the 10-year anniversary of the 2002 Olympics he helped lead there, his rival Rick Santorum attacked him for obtaining federal funding for the successful sporting event.

Romney’s appearance was an opportunity to underscore an argument he makes in nearly every speech, that he helped to orchestrate one of the most successful Winter Games after a damaging scandal marred the planning stages. It comes at a time when he has faced criticism not only for the Games’ price tag, but for taking too much credit for the turnaround.

Romney received a standing ovation at EnergySolutions Arena when he was introduced as CEO of the games at a “Stars on Ice” event marking the anniversary.

“Because of the strong leadership of the CEO, the fire that he lit within, these games were a tremendous success,” Kristi Yamuguchi said in introducing Romney.

Earlier, Romney, who was clad in a blue leather jacket emblazoned with USA 2002, spoke to a cheering crowd of former committee members, recalling how he was skeptical of joining the team at first — it was his wife Ann who convinced him. “For me the Olympics was one of those things that I saw on TV and I didn’t see why it was important for me to become involved in the games,” he said, adding that he finally came around after conversations with his wife.  “One of the things that drew me to the Olympics was that the games were a showcase for the great qualities of the human spirit.”

Meanwhile, former House speaker Newt Gingrich campaigned in Georgia, a state he represented for two decades in Congress, telling audiences he needs to win its primary next month if he is to regain momentum.

“I need your help,” Gingrich told an enthusiastic crowd at a Gwinnett County precinct meeting in Suwanee. “Some places we’ve won, some places we’ve lost, but we’re in the hunt. But it all hinges on Georgia.”

Romney and President Obama were the focus for Santorum as he campaigned in Ohio, a key swing state next door to his Pennsylvania home. The former Pennsylvania senator accused the president of embracing a belief system disconnected from the Christian faith.

Obama believes in a “phony theology — not a theology based on the Bible,” he told tea party supporters.

The Obama campaign called the statement “just the latest low” in a negative GOP nomination campaign, but Santorum told reporters the “new low” in the campaign is the Obama administration’s handling of the recent controversy over whether the national health-care law’s mandated coverage of contraception should apply to religious-affiliated institutions.

“The president has reached a new low in this country’s history of oppressing religious freedom that we have never seen before,” he told reporters after addressing a luncheon of the Ohio Christian Alliance. “And if he doesn’t want to call his imposition of his values a theology, that’s fine. But it is an imposition of his values over a church who has very clear theological reasons for opposing what the Obama administration is forcing on them.”

Santorum devoted most of his speech in Columbus to an attack on Romney’s role in the 2002 Olympics.

“One of the things he talks about the most is how he heroically showed up on the scene and bailed out and resolved the problems of the Salt Lake City Olympic Games,” Santorum told an enthusiastic group of about 300 tea party supporters gathered in a conference room an airport hotel. “He heroically bailed out the Salt Lake City Olympic Games by heroically going to Congress and asking them for tens of millions of dollars to bail out the Salt Lake Olympic Games. In an earmark. In an earmark for the Salt Lake Olympic Games.”

He added that John McCain, the Arizona Republican senator who has endorsed Romney, “called it potentially the worst boondoggle in earmark history.”

“Does the word hypocrisy come to mind?” Santorum asked the crowd, to applause.

Santorum’s focus on Romney comes as the Romney camp is continuing its assault on the former senator’s record in Washington, particularly his support for earmarks.

Santorum — who has surged in recent weeks and has a narrow edge over Romney in several national and state polls — defended the legislative pet projects Saturday, telling the crowd, “Let’s talk about the real issues of the day. . . . The idea that every earmark is a bad one is simply false.”

His campaign is hoping to capi­tal­ize on the ground he’s gained recently to make inroads not only in Michigan, which holds its primary on Feb. 28, but in several states voting on Super Tuesday, March 6. Kathy Hildebrand, Santorum’s field director in Georgia, stood outside as Gingrich addressed supporters in Suwanee and handed out fliers touting Santorum’s upcoming “God & Country Rally” Sunday night in nearby Cumming.

“The surge is just giving people the guts to go with their first choice, instead of settling for their second choice,” Hildebrand said, adding that when she’s been talking to voters in the state, “I told them it’s time we should let our votes determine the polls, not the other way around.”

Gingrich’s supporters said the former speaker continued to enjoy significant support in the area, though they acknowledged that Santorum has begun to attract the interest of some of their friends and neighbors.

“In Forsyth County, where we are, most people are for Newt. The entire state’s pretty much for Newt,” said Larry Mann, a retiree who attended a Forsyth County precinct meeting in Cumming. But, he added, “Santorum’s coming along pretty good.”

Gingrich, who held three events Saturday in the Atlanta area with former GOP presidential contender Herman Cain, described himself as a “real conservative” and “an effective conservative” who would enact a bold policy agenda as president.

Rather than spending much time discussing his Republican opponents, Gingrich hammered away at the idea that Obama is an elitist holding America back from tapping into its generous energy reserves. Noting that gas averaged $1.13 a gallon when he was House speaker, Gingrich pledged that he would bring gas prices down to $2.50 a gallon by allowing companies to drill offshore in more areas and to access oil and gas in shale deposits across the United States.

In a news conference Saturday morning, Gingrich said he had decided to emphasize the question of energy because “gasoline has reached a tipping point where people want to talk about energy more intensely.”

After a second event where he touted his energy plan, he told reporters, “The message works,” adding that it resonates with voters because “it fits their values.”

Staff writer Nia-Malika Henderson contributed to this report.