Photo
Supporters of Donald J. Trump watched the results of the New Hampshire primary on Tuesday in Manchester, N.H.CreditDamon Winter/The New York Times 
MOUNT PLEASANT, S.C. – — Donald J. Trump’s rivals for the Republican presidential nomination dug in Wednesday for a hard fight in the South Carolina primary, where Mr. Trump will seek to gain a clear upper hand in the 2016 race after his smashing victory in New Hampshire.
But the effort to stop Mr. Trump was only one element of the hard-edged, multifront campaign shaping up here among five candidates, nearly all of whom are facing immense pressure to demonstrate strength.
The Republican field after New Hampshire has clarified to two battles: between Mr. Trump and Senator Ted Cruz of Texas, the anti-establishment duo, and three establishment-friendly hopefuls. And on Wednesday, the contenders began exchanging fire in a way that underscored the complex calculations behind each of their candidacies.
Above all, there is a fight against Mr. Trump, which will be waged by Mr. Cruz and the mainstream candidates. After largely avoiding a sustained ad assault in New Hampshire, Mr. Trump is likely to face far more attacks here in a state known for its bare-knuckled politics. Mr. Cruz wasted little time Wednesday in signaling how he intended to run against the New York real estate mogul in the Bible Belt.
Photo
The Rev. Al Sharpton and Senator Bernie Sanders, fresh off his New Hampshire primary victory, met in Harlem on Wednesday. CreditSam Hodgson for The New York Times 
“The only way to beat Donald Trump is to highlight the simple truth of his record: It is not conservative,” he said in Myrtle Beach, highlighting his own ironclad conservative credentials. But in a sign of how he is facing challenges on two flanks, Mr. Cruz also began airing ads here against Senator Marco Rubio of Florida as well as Mr. Trump.
The Republican Party here is a lot like the party writ large. It is torn between activists enraged by President Obama and eager for the bald confrontation promised by Mr. Trump and Mr. Cruz, and party leaders hungry to take back the White House and considering candidates such as Mr. Rubio and Jeb Bush.
The contest here, coming on the heels of Mr. Cruz and Mr. Trump’s capturing the first two states, could help determine which of those two animating forces has more currency in the party.
Among the three mainstream Republican candidates, the Feb. 20 South Carolina contest appears to beh a race against Mr. Trump and a primary-within-a-primary among establishment candidates — Mr. Bush, Mr. Rubio and Gov. John Kasich of Ohio — to win the right to ultimately challenge Mr. Trump and Mr. Cruz.
Mr. Rubio and Mr. Kasich, swiftly criticized Mr. Bush for having spent so much money seeking to take down his opponents in the first two nominating states. And Mr. Bush, his once-forlorn campaign re-energized after outpolling Mr. Rubio in New Hampshire, made clear at a town hall meeting here that he would aggressively target the two establishment-aligned rivals he needs to defeat to consolidate the party’s support.
When a voter here asked him to distinguish himself from Mr. Kasich, Mr. Bush noted that the Ohio governor “led the charge” to expand Medicaidunder the Affordable Care Act. And without mentioning Mr. Rubio by name, the former Florida governor said voters should not embrace “a gifted politician that could give the most phenomenal speech,” but who lacks the experience to govern.
But Mr. Bush also intends to run what Senator Lindsey Graham, an ally, called “a referendum on who is ready to be commander in chief.” As Mr. Graham highlighted Mr. Kasich’s support for closing down military bases, Mr. Bush reserved his harshest rebukes for Mr. Trump. The former Florida governor drew applause and rueful head-shaking from an overflow crowd in this suburban Charleston town when he called out the party’s front-runner for having mocked John McCain, the winner of South Carolina’s 2008 primary, for his capture in the Vietnam War.
Continue reading the main story

After New Hampshire: Updates 

Injecting his stump speech with a new shot of urgency after Mr. Trump’s victory, Mr. Bush warned South Carolinians that the Republican Party’s identity was at stake.
“Our party is being hijacked by people who do not believe in the goodness of the conservative cause,” Mr. Bush said. “I do. I believe it.”
Mr. Rubio, too, signaled to reporters on his campaign plane that he would challenge Mr. Trump more assertively on his command of policy.
“I don’t think you can keep saying, ‘Trust me, I got a plan for it,’” Mr. Rubio said. “I think as we get closer, especially now that he’s been successful in New Hampshire, I would expect people will be pressing for more details.”
Even more than Mr. Bush, Mr. Rubio is grappling with how to confront multiple foes. And after his disastrous debate performance Saturday and a fifth-place finish in New Hampshire, the future of his campaign may ride on a South Carolina resurrection. The Florida senator is attempting to position himself as something of a hybrid candidate, acceptable to the establishment and to the hard right, so he is taking aim at Mr. Trump and Mr. Cruz while also re-engaging Mr. Bush.
The South Carolina campaign will take place in a state where political insurgencies of the sort represented by Mr. Trump and Mr. Cruz have often withered. For decades, South Carolina played the role of sorting out candidates aligned with the leadership of the national Republican Party, catapulting the winner of every primary here since 1980 to the presidential nomination, with one exception.
And that exception shows how South Carolina’s ability to select winners may be in flux. In 2012, voters here emphatically rejected Mitt Romney, the decisive victor in New Hampshire, and instead backed Newt Gingrich, who turned in two combative debate performances in the week leading to the primary.
Continue reading the main story

Graphic: 2016 Primary Results and Calendar 

Mr. Gingrich’s victory here reflected the state’s drift in recent years away from conventional Republican candidates and toward a more populist and at times purer brand of conservatism.
Still, the state’s voting rules may create some extra space for candidates outside the hard right. South Carolina does not register voters by political party, so any voter can cast a ballot in either the Democratic or the Republican primary, though not in both.
Mr. Kasich, whose second-place showing in New Hampshire was fueled by support from independents, is hoping to replicate such cross-party appeal in South Carolina but faces a far stiffer test here. He won about 16 percent of the vote in New Hampshire with a message crafted entirely to appeal to moderate Republicans and independent voters there and must show strength here to prove he is not a one-state wonder.
That pitch will probably have more limited appeal in South Carolina and across the next round of primary states, particularly if Mr. Kasich faces an advertising assault from Mr. Bush and the “super PAC” supporting him. He said on the plane from New Hampshire that any suggestion that he weakened the military is “kind of silly.”
But Mr. Kasich signaled at a town hall meeting in Charleston on Wednesday that he would not revise his message for a new audience.
“Some people try to call me a liberal because I think we should offer opportunity to everybody, not just to some people,” Mr. Kasich said. He shrugged off the criticism: “I don’t know how the Republican Party got so off kilter.”
Yet Mr. Kasich also sought to present himself as a plausible opponent for Mr. Trump. He twice brought up having outpolled Mr. Trump, three votes to two, in the tiny New Hampshire town of Dixville Notch.
Mr. Trump is already looking further down the primary calendar. He is scheduled to hold campaign stops this week in Louisiana and Florida, which do not hold primaries until March.
Should Mr. Trump win the South Carolina primary, it could grow exceedingly difficult for his rivals to slow his momentum as the race moves into a series of conservative states across the South the next few weeks.