COLUMBIA, S.C. — With Donald J. Trump’s decisive victory in New Hampshire and no strong runner-up among a pack of also-rans, the Republican race barreled into South Carolina on Wednesday shadowed by a question: whether any alternative candidate can gain enough support to threaten Mr. Trump’s drive to the nomination. Gov. John Kasich of Ohio, the second-place finisher in New Hampshire with less than half the support of Mr. Trump, arrives in this more conservative Southern state where he has little staff or support. Senator Ted Cruz of Texas, resuming an effort here to enlist the Christian right, the key...