Des Moines, Iowa (CNN) -- Coming off a barely-there victory in the Iowa causes, Mitt Romney vowed Wednesday he will continue to focus his campaign on defeating President Obama, rather than Rick Santorum.
Sixth-place finisher Michele Bachmann, meanwhile, scheduled a news conference for 11 a.m., ET, fueling speculation that she will withdraw from the race.
Santorum virtually tied Romney Tuesday in the nation's first nominating contest, coming in second by only eight votes in what appears to be the closest-ever margin of victory in a Republican presidential contest, the state Republican Party said early Wednesday.
"Of course, people are going to ask us about the differences on our positions on issues and backgrounds and so forth," Romney told CNN Wednesday morning. "But, really, if we talk about what the American people want to hear, it's how we're going to be different than President Obama when it comes to getting the economy going, preserving America's security abroad and making sure we rein in the scale of the federal government. "
The candidates' next contest will be in New Hampshire on Tuesday.
Romney said he was "feeling terrific, because, as you know, we were well behind several weeks ago," when polls suggested Newt Gingrich was in the lead in Iowa. "I don't think many people gave us a shot of beating" Gingrich, Romney said. "We obviously won last night, although it was very, very close,. Obviously, Rick Santorum and Ron Paul also had big nights. We all came out of Iowa a lot stronger. "
Ron Paul finished a close third, according to the state GOP.
"Game on!" Santorum tweeted. ""Thanks to all of you, we pulled off our #iowasurprise! Keep us going to NH, SC & beyond."
The South Carolina Republican primary is scheduled for January 21.
Santorum's website Wednesday automatically took visitors to a donation page celebrating the "Iowa Surprise" and saying Santorum proved "he is the only conservative who can beat Mitt Romney."
Paul, meanwhile, told CNN his success in Iowa shows "the message of liberty is appealing to everybody across the board."
In New Hampshire, he said, "I think we're going to have some momentum and we're going to continue to do what we're doing. It's a 'live free or die' state. They're very freedom-oriented,and that message will spread there. And I'm confident we will do quite well."
Despite a weak showing among voters in Iowa looking for a candidate they consider conservative, Romney told CNN he is confident that conservative voters will support him in New Hampshire.
Texas Gov. Rick Perry, who placed fifth in Iowa, said late Tuesday that he would return to his home state to consider whether his campaign would continue.
Romney, a former Massachusetts governor, had 30,015 votes. Santorum, a former U.S. senator from Pennsylvania and an upstart challenger who just weeks ago polled in the single digits, had 30,007, the state GOP said.
Each had roughly 25% of the vote in Iowa, the first state to vote in the 2012 presidential caucus and primary season. Paul, a U.S. representative from Texas, had 21%. Former House Speaker Newt Gingrich was at 13%. Perry was at 10%, Bachmann -- a Minnesota congresswoman -- had 5%, and former Utah Gov. Jon Huntsman had 1%.
State GOP officials said certified results will be released in two weeks.
The closest previous margin of victory in a GOP presidential contest was 257 in 1936, when Alf Landon won the 1936 South Dakota primary. In 2008, Barack Obama earned the closest-ever margin in a U.S. presidential contest, defeating Hillary Clinton by seven votes in the Guam caucus.
Speaking to supporters in Des Moines early Wednesday, before final results were known, Romney framed the Iowa contest as a "great victory" for him, Santorum and Paul.
"All three of us will be campaigning very hard to restore the heart and soul of this nation," Romney said.
On Wednesday, Sen. John McCain plans to travel to New Hampshire to endorse Romney, a senior Republican source close to the senator said. McCain beat Romney to win the Republican presidential nomination in 2008.
Romney has long been a front-runner in Iowa and most national polls, though he also has been stuck at roughly the same percentage of support as a revolving cast of conservative challengers bounced up and down, with Santorum the latest to rise.
Santorum told CNN early Wednesday -- before the final tally was announced -- that he would turn his attention to New Hampshire, where Romney, who governed neighboring Massachusetts, has had a large lead in polls.
"We're going to be on to New Hampshire. We're going to work hard and compete there," Santorum said. "I'm a little bit behind the curve in the sense that Gov. Romney has spent a lot of money and a lot of time up there, and has been running for six years. But we feel like we can go up there and compete."
Paul, speaking in Iowa late Tuesday, praised his supporters for a "fantastic showing" and claimed that he and the top two were the caucuses' "three winners," ready to raise money and compete well in the next contests.
"We have had a fantastic showing for this cause and challenging people ... and saying, you know, this challenge of, 'Let's go back to this real old-fashioned idea, this very dangerous idea: Let's obey the Constitution,'" Paul said. "... We will go on, we will raise the money. I have no doubt about the supporters."
Of the 25 pledged delegates at stake in Iowa, CNN estimates Romney, Santorum and Paul each won seven, with Gingrich and Perry winning two. The delegate number needed to clinch the nomination is 1,144.
The Iowa results typically are important because they give the top finishers the fuel they need, including fundraising, to keep their campaigns going. With Romney considered the runaway favorite in New Hampshire, some other candidates who continue past Iowa are expected to focus more on South Carolina, hoping to make a stand there.
Several candidates -- Santorum, Gingrich, Perry and Bachmann -- positioned themselves as conservative alternatives to Romney. As Gingrich's popularity in Iowa fell amid withering attack ads in December, Santorum rose just in time for the caucuses.
Obama, who is not expected to face a major challenge for the Democratic nomination, spoke to caucus-goers in an interactive video-teleconference to Democratic caucus sites Tuesday night.
He touted the end of the war in Iraq, health care reform and making college more affordable as some of his achievements — a similar message to the "promises" campaign video rolled out this week.
"In some ways, I'm more optimistic now than I was when I first ran, because we've already seen change take place," Obama said in the teleconference. "And part of what 2012 is about is reminding the American people how far we've traveled and the concrete effects that some of our work has had in terms of making sure people have health insurance and making sure our troops are coming home, or making sure people are able to go to college.
"Part of it is also framing this larger debate: What kind of country are we going to leave for our children and grandchildren?"
In addition to Perry, some other Republican candidates may now consider whether they're in position to compete in the upcoming contests.
One issue to watch will be how many of their supporters latch onto the remaining non-Romney candidates, said CNN political contributor Ari Fleischer, a former White House press secretary.
"Mitt Romney doesn't want anybody to drop out," Fleischer said Tuesday, suggesting Romney would want to have any anti-Romney vote split as many ways as possible. "Rick Santorum wants everybody to drop out."
Gingrich, whose popularity rose in Iowa late last year on the strength of his debate performances before the Iowa attack ads, said Tuesday night he would continue his campaign.
"I think that we are at the beginning of an extraordinarily important campaign," Gingrich told his supporters in Des Moines. "The goal of the campaign has to be to replace Barack Obama, but there will be great debate in Republican Party before we are prepared to have a great debate with Barack Obama."
Bachmann, who had hoped for better in Iowa, where she grew up and finished first in a GOP straw poll in the summer before dropping in the polls, also indicate her campaign would continue.
"There will be another occupant in the White House. Who knows, maybe even another Michele in the White House," she told supporters Tuesday night.
Before Bachmann spoke Tuesday night, CNN chief political analyst Gloria Borger said Bachmann would have to do some "soul searching" about whether to continue her campaign.
"She's not going to have the money to continue. She won the (GOP) straw poll in Ames in August ... She made a big point that she was born in Iowa, that this was going to be her state," Borger said.
Huntsman, a former U.S. ambassador to China, hasn't been competing in Iowa, choosing instead to focus efforts on New Hampshire.
Romney was the GOP front-runner in several major Iowa polls last week, with Paul second and Santorum third.
The Iowa caucuses began at 7 p.m. Tuesday in 809 locations after months of pitches from GOP candidates vying for the chance to take on President Barack Obama in Novembe
CNN's Peter Hamby, John Helton, Gabriella Schwarz, Shawna Shepherd, Paul Steinhauser, Shannon Travis, Jim Acosta, Jessica Yellin, Jason Hanna and Keating Holland contributed to this report.