BEDFORD, N.H. — Ohio Gov. John Kasich vowed to build on his strong showing in the New Hampshire presidential primary, and Donald Trump said he is prepared to face dirty campaigning as a slimmed-down Republican field shifted to South Carolina on Wednesday.
New Jersey Gov. Chris Christie and businesswoman Carly Fiorina suspended their bids after failing to gain traction, leaving a clearer fight between the insurgents and the establishment of the Republican Party. South Carolina, with its military roots and large population of social conservatives, is poised to settle both of those battles.
Mr. Trump arrived in the state Wednesday night after easily winning New Hampshire, saying he was operating on one hour of sleep and extolling polls that showed him with a significant lead.
“We’re through the roof. We are high,” he said in Pendleton.
He is in a showdown with Sen. Ted Cruz, who won Iowa’s caucuses, finished third in New Hampshire and said he proved he is the best person to take on Mr. Trump.
“This is a national campaign, and one of the most important conclusions coming out of these first two states is that the only candidate who can beat Donald Trump is me,” Mr. Cruz told reporters.
On the establishment side, former Florida Gov. Jeb Bush was counting on his family legacy to rescue him, running ads featuring his brother, former President George W. Bush. Sen. Marco Rubio, Florida Republican, said he will try to recover from his stumble in Saturday’s debate at the hands of Mr. Christie.
Meanwhile Ohio Gov. John Kasich, who surprised analysts with a strong second-place showing in New Hampshire, must decide quickly on the states where he can compete and build a low-budget organization.
He credited his performance in New Hampshire to his lower-key approach but said he is not going to recoil if his campaign is attacked.
“Well, look, if somebody pounds me, I’m not going to taking a pounding. I’m not some kind of a pin cushion or a marshmallow,” Mr. Kasich said on “CBS This Morning.” “But look, I think people are tired of the negativity.”
Republican analysts say Mr. Kasich faces an uphill battle to stay viable that long, particularly with Mr. Rubio and Mr. Bush also still in the race and headed for a showdown in South Carolina.
“I don’t think it is realistic to expect anything out of John Kasich in South Carolina,” said Bruce Haynes, a Republican strategist. “What New Hampshire did was extend the life of the Bush campaign and set South Carolina up as a test that Rubio needs to pass.”
Mr. Haynes said Saturday’s debate in South Carolina could further define the race and that Gov. Nikki Haley could sway voters with an endorsement.
“She’s popular and deeply respected, and her endorsement of one of the other candidates would drive that candidate’s ability to dominate the news and could give them a big boost,” he said.
Retired neurosurgeon Ben Carson finished in eighth place in New Hampshire, but he pointed out that he didn’t spend as much money in New Hampshire as other candidates.
“We’re doing just fine,” Mr. Carson said on CNN. “People continue to support us. We will continue to move forward.”
He is likely to face increasing calls to follow Mr. Christie and Mrs. Fiorina, who exited the race after it was clear that they wouldn’t qualify for the debate this weekend.
“While I suspend my candidacy today, I will continue to travel this country and fight for those Americans who refuse to settle for the way things are and a status quo that no longer works for them,” Mrs. Fiorina said in a statement on Facebook.
Mr. Christie also made his official exit announcement on Facebook.
“I leave the race without an ounce of regret,” he said. “I’m so proud of the campaign we ran, the people that ran it with me and all those who gave us their support and confidence along the way.”
Mr. Christie had everything riding on New Hampshire, where he hoped the time he invested would translate into enough support at the ballot box that he could convince voters that he is the most viable alternative to Mr. Trump and Mr. Cruz.
The New Jersey governor entered the race with high hopes that his self-declared penchant for tough talk would resonate with voters. But Mr. Trump outbid him on that score. He also struggled to rebuild his image in the wake of the 2013 “Bridgegate” scandal.
Mr. Christie’s most memorable moment of the campaign was during the eighth Republican presidential debate over the weekend, when he landed devastating blows against Mr. Rubio for being overly scripted and too inexperienced to be president and warned that President Obama should serve as a cautionary example about what happens when the nation elects a first-term senator.
New Hampshire voters said the episode led them to rethink their support of Mr. Rubio and give Mr. Christie another look.
The results Tuesday, though, showed that it ended up being too little too late.
As reports of Mr. Christie’s decision surfaced, Rep. Trey Gowdy, South Carolina Republican, said the New Jersey governor effectively helped the Democrats with his attack on Mr. Rubio.
“What Chris Christie did was an in-kind contribution to the Democrat Party,” Mr. Gowdy, who has endorsed Mr. Rubio, said on Fox News. “There was no chance that Chris Christie was ever going to be our nominee, and he’s certainly not going to do well in South Carolina if he bothers to come.”
• David Sherfinski reported from Washington.
• Seth McLaughlin can be reached at smclaughlin@washingtontimes.com.
• David Sherfinski can be reached at dsherfinski@washingtontimes.com.
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