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MYRTLE BEACH, S.C. – Senator Ted Cruz said on Wednesday that the Republican race was narrowing to a two-man contest and that the only way for the party to stop Donald J. Trump from winning the nomination was for conservatives to unite behind him.

“One of the most important conclusions coming out of the first two states is the only candidate that can beat Donald Trump is me,’’ Mr. Cruz said, after exceeding expectations in New Hampshire, where Republican voters are more moderate than in Iowa or South Carolina.

The Cruz campaign has long sought a one-on-one contest with Mr. Trump, convinced the Texas senator’s arch-conservatism is better aligned with the party’s base. But after Marco Rubio’s strong third-place finish in Iowa, a three-man contest suddenly spoiled that plan.

Mr. Rubio’s poor showing on Tuesday night, fifth behind Jeb Bush, dealt a blow to the Florida senator as he sought to consolidate support from the party’s establishment. Yet, by breathing life into Mr. Bush’s candidacy as the race arrives here — where being a Bush is not the burden it is elsewhere – the group of four New Hampshire also-rans, including Gov. John R. Kasich of Ohio, may simply split the stop-Trump vote too many ways.

That is what Mr. Cruz needs to overcome, and South Carolina’s many evangelical and conservative voters offer him that opportunity.

“The only way to beat Donald Trump is to highlight the simple truth of his record – it is not conservative,’’ Mr. Cruz said, a statement that may be equal parts strategy and wishful thinking. The road to a Cruz upset here, where Mr. Trump has the same double-digit polling lead he held in New Hampshire, will not be easy.

Mr. Cruz plans to spend every day in the state until the Feb. 20 primary. At his first rally after arriving here, he boasted of having nearly 10,000 volunteers in South Carolina, a reprise of the intensive field organization that won him Iowa. Wearing red “Cruz Crew” T-shirts, his volunteers filled the front rows of a theater a few blocks from the Atlantic Ocean. They leapt to their feet frequently to applaud, even as other attendees remained seated while clapping.

But despite the demographic similarities between South Carolina and Iowa that favor Mr. Cruz, Mr. Trump will find it easier to turn out supporters in the state’s primary compared with the Iowa caucuses, where his ground game failed him.

Mr. Cruz began his speech Wednesday with a familiar salutation: “God bless the great state of South Carolina.” He asked supporters to bring nine friends to the polls. That way, he said, “each of you will have voted 10 times.’’