In South Carolina, Gov. Nikki R. Haley, the state’s first nonwhite governor, and Senator Tim Scott, the first black senator elected from the South since Reconstruction, have both backed Senator Marco Rubio of Florida as an alternative to Mr. Trump. The picture of the three of them campaigning together “says a lot about the Republican Party,” Mr. Rubio, who is of Cuban descent, said in an appearance on CNN on Wednesday.

The fear among Republican leaders here is that a smashing victory for Mr. Trump would say more about the party, and about the state, potentially undermining South Carolina’s image as a more welcoming place that is no longer defined by figures like Strom Thurmond, the former segregationist presidential candidate who served in the Senate until 2003.

Former Gov. David M. Beasley, a Republican who sought unsuccessfully to bring down the Confederate flag during his single term in office, said Mr. Trump’s campaign had given voice to a “serious sense of frustration” in the state. But he said the Trump message was not a fair approximation of South Carolina values.

“It does not reflect South Carolina,” said Mr. Beasley, who has not endorsed a candidate in the race. He added, “Trump has been very divisive, and it’s a strategy that he has taken to be, clearly, a non-establishment candidate.”