Washington (CNN) -- Newt Gingrich conceded Sunday that losing his home state of Georgia in the Super Tuesday primaries in March would "badly" weaken his candidacy.
Appearing on "Fox News Sunday," Gingrich added that if either of his chief rivals for the Republican presidential nomination lose their home states -- Mitt Romney in Michigan and Rick Santorum in Pennsylvania -- they also would be "badly, badly weakened."
However, Gingrich stopped short of saying he would drop out if he fails to win Georgia on March 6.
"Given the chaos of this race, I'm not willing to say anything," Gingrich commented, adding: "I think it's extraordinarily important to win your home state."
Romney faces the first test, with Michigan's primary on February 28. The Pennsylvania primary is on April 24.
The dynamic of the Republican race has continually shifted, with Romney's position at or near the top the only consistent factor.
However, the former Massachusetts governor has been unable to broaden his support through the early primaries, while Santorum has surged in recent weeks to supplant Gingrich as Romney's main conservative challenger.
The latest results from Gallup's daily tracking poll showed Santorum now leads Romney among registered Republicans nationwide.
According to the poll released Sunday, 36% of respondents backed Santorum while 28% preferred Romney.
The new numbers represented a five-point drop for Romney since Wednesday, when the former Massachusetts governor was statistically tied with Santorum, who increased by five points in the same period.
Gingrich, meanwhile, has seen his poll numbers decline over the past month since his only primary win in South Carolina on January 21.
According to Gallup, Gingrich came in third place in Sunday's poll with 13%, with Texas Rep. Ron Paul closely behind at 11%.
Perhaps emboldened by his increased support, Santorum has launched a series of harsh attacks on President Barack Obama in recent days.
He drew the ire of Obama's campaign Sunday by declaring the government should never require health care providers to fully cover the cost of prenatal testing such as amniocentesis, which can determine the possibility of Down syndrome or other problems in the fetus.
In particular, amniocentesis "more often than not" results in abortion, said Santorum, a strident anti-abortion politician, on the CBS program "Face the Nation."
"People have a right to do it, but to have the government force people to provide it free just is a bit loaded," Santorum said in arguing against what he called a mandate in the health care reform bill passed by Obama and Democrats in 2010.
Santorum was responding to questions about comments he made the day before at a Christian Alliance luncheon in Columbus, Ohio, in which he said the mandate in the health care law was intended to increase abortions and reduce overall health care costs.
Lis Smith, a spokeswoman for Obama's campaign, called Santorum's remarks "the latest in a long string of unfortunate comments in the race to the bottom that the Republican presidential primary has become."
"Prenatal screenings are essential to promote the health of both the mother and baby and to ensure safe deliveries," Smith said. "These misinformed and dangerous comments reinforce why women cannot trust any of the Republican candidates for president."
Also Saturday in Columbus, Santorum appeared to raise questions about Obama's adherence to Bible-based Christian theology in comments that Obama campaign spokesman Robert Gibbs said went "well over the line."
Santorum said Saturday the president was adhering to "some phony ideal, some phony theology," which he described as "not a theology based on the Bible, a different theology. But no less a theology."
Later asked by reporters about the remark, Santorum said he was trying to say Obama merely holds "different moral values."
Obama has reached a "low in this country's history of oppressing religious freedom that we have never seen before," Santorum added.
Gibbs, appearing Sunday on the ABC program "This Week," said Santorum's comment continued the kind of character attacks that he noted have characterized the Republican presidential race so far.
"I think that if you make comments like that, you make comments that are well over the line," Gibbs said. "I think this GOP primary, in many cases .... has been a race to the bottom. We have seen nastiness, divisiveness, ugliness, distortions of opponents' records, of the president's records."
The negative tone of the campaign was hurting the Republican candidates and causing low turnout numbers in some of the primaries so far, Gibbs added.
"It's just time to get rid of this mindset in our politics that, if we disagree, we have to question character and faith," Gibbs said. "Those days have long passed in our politics. Our problems and our challenges are far too great."
Republican Sen. John McCain of Arizona, who lost to Obama in the 2008 presidential election, agreed that persistent infighting among Republicans was hurting the party's cause and image.
"I've been in very tough campaigns. I don't think I've seen one that was as personal and as characterized by so many attacks as these are," McCain said on the ABC program "This Week."
He blamed the influence of super PACs that can spend unlimited amounts on campaign ads, adding: "I do not believe I've ever seen campaigns characterized overwhelming(ly) by negative attacks."
Santorum's comments may appeal to some Republican voters who have questioned Obama's faith before, or others who saw the administration's recent contraception mandate as an overreach.
Democratic Rep. Chris Van Hollen of Maryland told the NBC program "Meet the Press" that Santorum and other Republicans were seeking to shift the political debate to social issues because the latest reports showed Obama's economic policies were helping the nation recover from recession.
"What you're seeing here is that as the economy is improving and more and more people are going back to work, and it's clear that the president's policies on the economy are working, you find Republicans going back to the old red meat social issues that helps rile up their base," Van Hollen said. "That's what is going on."
On the same program, Republican Rep. Paul Ryan of Wisconsin said the issue was Obama's attempt to expand government powers beyond what was intended by the Constitution on issues such as the health care reform law of 2010.
"If the president is willing to trample on our constitutional rights in a difficult election year, imagine what he will do in implementing the rest of this law after he doesn't have to face the voters again if he gets re-elected?" Ryan said.
Meanwhile, Paul took aim at Santorum on Sunday by questioning his conservative credentials and doubting if the former Pennsylvania senator could beat Obama in November if he wins the party's nomination.
"His voting record is, I think from my viewpoint, an atrocious voting record -- how liberal he's been in all the things he's voted for over the many years he was in the Senate and in the House," Paul said of Santorum on CNN's "State of the Union."
Paul has previously attacked Santorum for voting for raising the debt ceiling five times as a senator, as well as the infamous "Bridge to Nowhere" in Alaska that was considered unnecessary government spending.
While Paul has yet to win any state contests, unlike the other three GOP presidential contenders, he reiterated he was still in the race for the long haul, anticipating a run that could extend to the Republican National Convention.
Gingrich, who is under pressure from the political right to drop out to consolidate conservative support behind Santorum, told reporters Sunday he also expects a long campaign.
"I tell people it's like the NCAA Final Four with no elimination," Gingrich said in reference to the annual college basketball tournament known as March Madness, adding: "You could imagine all of us going all the way to the convention."
CNN's Ashley Killough, Athena Jones and Gregory Wallace contributed to this report.