But New Hampshire is much friendlier territory for real-estate magnate Donald Trump, who heads into the votes with a commanding, double-digit lead.
In the Democratic primary, meanwhile, Sen. Bernie Sanders (I-Vermont) has continued to surge. After a narrow loss to the front-runner, former Secretary of State Hillary Clinton, in Iowa, Sanders is poised to capture victory in the Granite State. Clinton still holds a sizable, if shrinking, lead in national polls.
Here's another look at who has the best chance of making it to the White House to succeed President Barack Obama.
Our rankings are based on the Real Clear Politics averages of national polls and those in states of New Hampshire and South Carolina. We also factored in the candidates' delegate count and their finish in Iowa, as well their momentum (or lack thereof) over the past few weeks.
Since Iowa, four candidates have dropped out of the race: former Arkansas Gov. Mike Huckabee (R), Sen. Rand Paul (R-Kentucky), former Sen. Rick Santorum (R-Pennsylvania), and former Maryland Gov. Martin O'Malley (D).
Here's a look at where all the candidates stand.
All poll results as of Monday.
Feb 2016 Presidential Power Rankings
POWER RANKINGS: Here's who has the best chance at being our next president
10. Carly Fiorina, Republican, former Hewlett-Packard CEO
But over the past few months, she has had trouble sustaining that magic amid more scrutiny. She has dipped from her third-place standing in national polls at the height of her climb to a paltry 2.5% now. She was the only major Republican candidate to fail to qualify for last weekend's debate.
Still, she has experience as a business executive that few others in the field can point to, and she has been one of Hillary Clinton's fiercest critics.
National polling average among Republican voters: 2.5% (T-7th)
New Hampshire: 4.7% (7th)
South Carolina: 1.7% (8th)
His national poll numbers have dipped about 17 points over the past three-plus months.
National polling average among Republican voters: 7.8% (4th)
New Hampshire: 2.9% (8th)
South Carolina: 8.7% (5th)
Last month: 9
(AP Photo/Chris Carlson)
8. Chris Christie, Republican, New Jersey governor
Christie has seen a bit of momentum sapped over the past month in the first-primary state of New Hampshire, where he is counting on a strong finish and where he has put in the most time of any GOP candidate.
Amid a barrage of attacks from rival candidates and their allied interests, Christie has seen his poll standing in the Granite State dip about six points over the past month-plus. He's now sixth there, compared with fourth last month.
He had, however, the most attention-grabbing moment of last weekend's debate, when he confronted Rubio and got the best of him during a lengthy, terse exchange. He has argued that exchange has the potential to alter the fundamentals of the race. We'll see.
National polling average among Republican voters: 2.5% (T-7th)
New Hampshire: 5.4% (6th)
South Carolina: 2.3% (6th)
Last month: 8
(Photographer: Andrew Harrer/Bloomberg via Getty Images)
7. John Kasich, Republican, Ohio governor
Kasich might be positioned well to finish within the top three spots in New Hampshire, a feat that would be a serious boon to his ambitions to hang around in the race. After Rubio's debate stumble, there's a legitimate chance he could come out on top of a clustered bit of Republican establishment-type candidates.
Those who talk up Kasich believe he is a Christie-type without the baggage of the past year and a half — that is, a successful governor with a record to point to and clear bipartisan appeal. He also has a plethora of experience from serving nearly two decades in Congress, including foreign-policy areas and his time as chair of the US House budget committee.
But that same bipartisan brand could hurt Kasich with the GOP base beyond New Hampshire. He is to the left of most GOP candidates on immigration reform, and he expanded the federal Medicaid program under the Affordable Care Act — two issues that could doom him with hard-line conservatives.
National polling average among Republican voters: 4% (6th)
New Hampshire: 13% (3rd)
South Carolina: 2% (7th)
Last month: 7
(AP Photo/Matt Rourke)
6. Jeb Bush, Republican, former Florida governor
AP Photo/Charles Krupa
Bush, once viewed as the clear front-runner, has seen Trump sap the momentum he had built after his official campaign announcement in June. His poll numbers have slumped across the board — his 17% national average in July has dipped almost 13 points over the past six-plus months.
It's starting to pay off, as he has seen a slight poll bump over the past few weeks in New Hampshire, and now sits in fifth amid a crowded cluster of establishment-minded candidates.
Bush has showed, too, that he is a dynamic fund-raiser. And he retains significant resources that could prove to be a game changer in the long haul.
National polling average among Republican voters: 4.3% (5th)
New Hampshire: 11.3% (5th)
South Carolina: 10% (4th)
Last month: 5
(Photo by Scott Eisen/Getty Images)
5. Bernie Sanders, Democrat, senator from Vermont
Sanders looks poised to upset Clinton in New Hampshire — perhaps by a significant margin — a feat that was unthinkable even last summer.
Sanders is peaking at the right time. His momentum, and the grassroots support and donations behind it, have evoked comparisons to the 2008 rise of Barack Obama, then an Illinois senator.
But Sanders still faces daunting challenges against the behemoth that is Clinton and her campaign. There are questions about whether he's a legitimate threat in the long haul and about his viability as a potential nominee in a general election.
But the door to the nomination that was long thought closed could creak even more open with a strong win in New Hampshire.
National polling average among Democratic voters: 36% (2nd)
New Hampshire: 53.9% (1st)
South Carolina: 32.5% (2nd)
Last month: 6
(Photo by Andrew Burton/Getty Images)
4. Marco Rubio, Republican, senator from Florida
Rubio was perhaps the biggest winner from the Iowa caucuses, as he and his campaign played the "expectations game" perfectly and surprised with a stronger-than-expected, third-place finish right behind Trump.
He has surged in the week since. He's up more than six points nationally and about four points in New Hampshire. He looked poised for a strong second-place finish, in fact, until last weekend — when he earned brutal reviews for his debate performance.
Did his rivals bring him down a notch? Rubio's finish in New Hampshire could perhaps define the shape of the race going forward.
National polling average among Republican voters: 17.8% (3rd)
New Hampshire: 14.4% (2nd)
South Carolina: 12.7% (3rd)
Last month: 4
(Photo by Chip Somodevilla/Getty Images)
3. Ted Cruz, Republican, senator from Texas
Cruz rode a record turnout in Iowa — something that was supposed to benefit Trump — to a surprisingly robust victory. He has built momentum heading into his target — the "SEC primary" states in the South, many of which vote March 1.
Cruz's under-the-radar campaign has put him in sneakily good position to capture the nomination. And his eye-popping fund-raising numbers mean he will most likely be in the race for the long haul.
Cruz inspires a flood of enthusiasm among the GOP base, and he may be the best-positioned candidate from within the political sphere to back up the notion that he's not a typical politician, that he is the outsider the base wants despite his day job in Washington.
National polling average among Republican voters: 21% (2nd)
New Hampshire: 12.4% (4th)
South Carolina: 19.7% (2nd)
Last month: 3
(AP Photo/Robert F. Bukaty)
2. Donald Trump, Republican, businessman
Trump has lit the political world on fire since his entry into the race last summer. And he has showed surprising staying power — we're now on month No. 9 of the Trump show.
He lost in Iowa. But the Hawkeye State was never fertile ground for someone like Trump, a brash New York billionaire. A solid win in the Granite State would do wonders toward getting his campaign back on winning footing.
There's a clear appetite among Republican primary voters for someone like Trump, who entered the race to controversy surrounding his position on illegal immigration. Business Insider discovered more of that when we followed him on the trail for a week last year.
National polling average among Republican voters: 29.5% (1st)
New Hampshire: 30.7% (1st)
South Carolina: 36% (1st)
Last month: 2
(AP Photo/David Goldman)
1. Hillary Clinton, Democrat, former secretary of state
Clinton is No. 1 here because she has proved formidable in polling and fund-raising and has a clearer path to the nomination than anyone on the GOP side.
But Clinton is facing an increasingly rugged challenge from Sanders, who threatens to win easily a state she captured in 2008. In fact, the race is starting to draw some 2008 comparisons — with her husband, former President Bill Clinton, on the attack, and rumors of a potential staff shake-up in the works.