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Republicans took some solace in the fact that they elected Ted Cruz to the Senate, adding another high-profile Hispanic to their roster, which already includes two Hispanic governors and two Indian-American governors.

Still, the GOP is searching for answers when it comes to black voters.

Pat Mullins, chairman of the Republican Party of Virginia, said the problem isn’t GOP principles.

“I’ve sat and talked when I was in Fairfax with the NAACP — we were right there on everything,” said Mr. Mullins, who served as chairman of the Fairfax County Republican Committee from 1990 to 1996. “[The head] was pro-life, he was concerned about the education his kids were getting, they wanted access to guns in their neighborhood, they were concerned about drugs, the small-business people in his community needed help. I mean, it was bang, bang, bang — we didn’t have a thing that we disagreed with at all. But we haven’t communicated — and that’s what we need to talk about.”

Mr. Mullins added that the problem is fundamentally deeper than simply putting up minority candidates to run.

“That, to me, is almost condescending,” he said, adding that the way to reach out was through message. “It’s a philosophy-type thing — ‘This is where we are, where are you? What do we need to do to help you out a little more?’”

That was the same message the GOP’s black candidates took into their races.

Ms. Love nearly toppled six-term incumbent Rep. Jim Matheson in Utah, losing by little more than 1 percent, while Mr. Parker ran 4 points behind Democrat Kyrsten Sinema in Arizona.

Mr. Scott easily won his race, leading his Democratic opponent by more than 25 points.

Mr. Davis said Ms. Love and Mr. Parker have both left themselves in good stead for future runs for office, and he said the GOP’s model for recruitment and advancement remains sound.

Love, Parker, West, and for that matter Tim Scott have all distinguished themselves by building a career that rested on their credentials and their beliefs, not their color; the same obviously can be said of Condi Rice,” Mr. Davis said. “This approach is a far better role model for black Republicans than becoming racial special advocates for one community, and it is exactly the model that successful Indian and Latino Republicans have followed.”