(CNN) -- With the Iowa caucuses and the New Hampshire primaries now history, the Democratic and Republican presidential races are still wide-open contests that will force candidates to continue to battle over the next four weeks.
Sens. Hillary Clinton and John McCain, the big winners in the New Hampshire primary, and the rest of the candidates did not rest on their laurels Wednesday as they began looking ahead to the next primary contests in Michigan, Nevada and South Carolina.
Clinton's two percentage-point win over Sen. Barack Obama in the Granite State's Democratic primary, after she came in third in the Iowa caucuses, had supporters chanting "comeback kid" when she took the stage to claim victory Tuesday night.
With 96 percent of the precincts counted, Clinton beat Obama 39 percent to 37 percent, a surprise win as polling going into the night had Obama leading the New York senator by 9 percentage points. John Edwards come in a distant third at 17 percent.
Clinton's victory means she and Obama will battle for front-runner status as the campaigns turn their focus to the Nevada caucuses on January 19, the South Carolina primary on January 26, the Florida primary on January 29 and the nearly two dozen states that will hold caucuses or primaries on February 5. Watch the candidates declare victory in New Hampshire »
"It was a great moment for me, and I think it really demonstrated what the people of New Hampshire have [done] time and time again," Clinton said from her home in Chappaqua, New York, where she had a brief rest before heading out on the campaign trail again.
"They take a hard look at everybody. They ask a lot of tough questions, and they render their judgment. They're famously independent, and they sure showed it last night."
The former first lady heads next to South Carolina to drum up support there.
McCain's victory in the Republican New Hampshire primary Tuesday night revealed how the race for the GOP presidential nomination has no clear front-runner and is even more open than the Democratic contest. Read how CNN's analysts view the results from New Hampshire »
The Arizona senator topped Mitt Romney 37 percent to 32 percent, with 96 percent of the precincts reporting. Mike Huckabee, the winner of the Iowa caucuses, came in third with 11 percent.
McCain's New Hampshire win will likely result in an infusion of cash that will allow him to wage an effective campaign in the upcoming primaries, analysts told CNN.
McCain, whose campaign was written off by many political pundits this summer after he had to lay off staff due to a poor fundraising, was greeted by the crowd with cheers of "Mac is back" when he made his victory speech Tuesday night. View pictures from primary night »
"I'm past the age when I can claim the noun 'kid,' no matter what adjective precedes it, but we sure showed them what a comeback looks like," the 71-year-old, four-term senator said.
The Republican candidates now turn their attention to the Michigan primary on January 15, the South Carolina caucuses on January 19, and the Florida primary on January 29.
Hoping to exploit his momentum, McCain campaigned in Grand Rapids, Michigan, Wednesday. Watch McCain call himself the 'underdog' »
The Michigan contest is shaping up to be a repeat of the New Hampshire battle between McCain and Romney, a former Massachusetts governor. Having lost both the Iowa and New Hampshire contests after spending nearly $7 million in advertising in both states, a win in Michigan is particularly important for Romney, whose father was governor there in the 1960s.
"We're not going to pull back. We're going to win Michigan," Romney told supporters In a conference call with supporters Wednesday morning, noting that he was won more votes and delegates than any other Republican nominee so far.
"I've got the lead now," Romney said. "I'm in first place."
Romney told backers he thought he would win in Michigan because both he and his wife, Ann, were born there and because the state's voters "will want someone who can pull them out of the recession."
"Michigan is a state going through a one-state recession," he said. "If I am president, that one-state recession is over."
South Carolina, where McCain's 2000 campaign effectively died, could present a challenge for him. One of every three voters in the 2000 GOP primary was a self-described member of the religious right, and they supported George W. Bush over McCain, 68 percent to 24 percent. On the other hand, 27 percent of voters in the 2004 primary were veterans, like McCain.
To win South Carolina, McCain will have to best Huckabee, who has been polling with a double-digit lead over him among a Republican electorate that is heavily dominated by social conservatives.
Huckabee, a former Arkansas governor and Baptist preacher, enjoyed strong support from evangelicals in Iowa, who made up 60 percent of caucus-goers.
Former Tennessee Sen. Fred Thompson has also been courting social conservatives and campaigning heavily in the Palmetto State. Thompson campaigned in South Carolina on Tuesday rather than in New Hampshire.
Now that the first two opening contests of the primary season are complete, candidates Wednesday were re-assessing their strategies, including the Clinton campaign.
Analysts expect the Clinton camp to trot out her husband at more campaign appearances.
Solid support from women was crucial to Clinton's narrow victory over rival Barack Obama, CNN senior political analyst Bill Schneider
"If I had a single word, the word would be 'women,' " Schneider said. "She got the women back."
Pundits think that a glimpse of emotion she offered voters a day before the primary helped soften her image and may have swayed undecided women voters. Clinton teared up while answering a question Monday about how she keeps herself together amid the rigors of campaigning.
"You know, I have so many opportunities from this country, I just don't want to see us fall backwards," she said, her voice breaking a bit. The audience applauded.
Obama said Wednesday that his message of change will continue to resonate with voters as he pursues the Democratic nomination.
"We feel great [about] what we've been seeing between Iowa and New Hampshire -- record turnouts, people extraordinarily engage in the process." Obama told CNN. "What's clear is that the American people are taking this process seriously.... They want to bring about a fundamental change on how our politics works here in this country. So we think that serves our campaign well and will serve the American people well once I'm president."
Obama hopes to regain the momentum with a victory in Nevada. On Wednesday the powerful Service Employees International Union of Nevada endorsed the Illinois Democrat.
The union's Executive Vice President Shauna Hamel said the "overwhelming participation" of voters in the Iowa caucus and the New Hampshire primary showed that "Americans are ready for change."
Obama's victory in Iowa may lead Democratic voters who had been leaning toward Clinton to reconsider him because they did not think think Obama was electable, experts say.
On Wednesday, Obama plans to stump in Jersey City, New Jersey, just minutes from New York City and not far from Clinton's home. He then plans to swing into Manhattan for a campaign fundraiser.
After his second place finish in Iowa, Edwards tracked a distant third in the New Hampshire primaries. The former North Carolina senator hopes a strong showing in either Nevada or South Carolina can put him back in contention.
The race is far from over, Edwards said Tuesday night.
Only about 1 percent of Americans had voted so far, he said, and the other "99 percent deserve to be heard."
"I'm in this race to the convention, where I intend to be the nominee of my party," he said. E-mail to a friend
CNN's Alexander Marquardt contributed to this report.