Republican presidential candidates, from left, Sen. Ted Cruz (Tex.), retired neurosurgeon Ben Carson and Sen. Marco Rubio (Fla.) stand in contrast to the Democrats’ all-white presidential field. (Charlie Neibergall/AP)

Juan Rodriguez, a Colombian immigrant and Republican businessman in Des Moines, is on a mission to persuade his employees, nearly all Hispanic Democrats, to elect a president from what they think of as the party of white guys.

This year, with three minorities among the top four GOP contenders, Rodriguez thought he had a shot. “You are against abortion, yes? Against same-sex marriage, yes?” he tells them. “Then you are a Republican!”

“No, no,” comes the response. The workers can’t get past what they hear from some Republican candidates about immigrants and immigration. They respond, in other words, with what many Republicans have long argued — that ethnic identity is not as important as what candidates stand for.

After years of deriding Democrats for dividing Americans into hyphenated subgroups, Republicans face a tantalizing and vexing prospect this year. With two sons of Cuban immigrants, Marco Rubio and Ted Cruz, joining a famed African American surgeon, Ben Carson, near the top of the polls, they have a unique opportunity to reach out to minorities as the party has long wanted to.

Some party officials say the Republicans’ more diverse field of candidates — especially in contrast to the Democrats’ all-white list — is evidence of conservatism’s broadening appeal. But others, loath to adopt the identity politics they associate with liberalism, maintain that the focus must stay on conservative ideas rather than the ethnicity of the people touting them.

“The fact that you have Latinos and a black among the leading candidates is just coincidence,” said J.C. Watts, a former Oklahoma congressman who became one of the nation’s most prominent African American Republicans. “It doesn’t speak to what’s beneath the surface. We’re still not talking about the concerns of that young black couple starting a business or that young Hispanic family,” he said, adding: “Where are our solutions to deal with incarceration reform, unemployment, the trouble blacks and Hispanics have getting home mortgages? Republicans who ignore Ferguson and Baltimore and Black Lives Matter are refusing to hear the depths of what people are experiencing.”

The GOP’s quandary has surfaced three years after the official autopsy of Mitt Romney’s 2012 defeat concluded that Republicans must persuade a rapidly diversifying electorate that the party is not scary or narrow-minded. But that effort is more complicated for the GOP than for Democrats, who have eagerly tapped into identity politics, mobilizing minorities to help elect the first black president and, now, emphasizing the historic potential of making Hillary Clinton the first woman to hold the job. The Republican calculus has been made even more complex by front-runner Donald Trump’s sharp rhetoric about immigrants and black activists.

The Republican National Committee has invested heavily in outreach to Hispanic voters in the past three years, with 40 Hispanic staffers connecting with business leaders and showing the party flag at community events. The Libre Initiative, funded by the billionaire Koch brothers, is touting the benefits of the free market and smaller government on Spanish-language radio stations and at neighborhood health fairs and food giveaways in states with large Hispanic populations. A similar, party-funded effort called Committed to Community woos black voters with church events, concerts and ads on black-oriented radio stations.

But Republicans’ efforts to broaden their appeal seem to run smack up against many conservatives’ belief that too much of a focus on group identity detracts from American unity — that what comes after the hyphen in any ethnic-American identity risks ­becoming overshadowed by the front end.

Rubio, Cruz and Carson avoid emphasizing their ethnicity as a selling point. Rather, they tell their family stories of upward mobility — an effort to connect to a universal American narrative of assimilation rather than what they see as a separatist instinct on the other side of the nation’s ideological divide.

Rubio’s spokesman, Alex ­Conant, said his candidate actively seeks Hispanic votes by doing interviews with Spanish-language media but “he delivers the same message as he does in English. We have a president who for eight years has tried to pit Americans against each other. ­Rubio is more interested in speaking to all Americans, not just to one group.”

Similarly, “Cruz talks about his father’s story, from dishwasher to having a son who’s a candidate for president,” rather than about being Hispanic, said campaign spokesman Rick Tyler. “If the answer is to be the party of identity politics, then we’ll just lose. There’s nothing for us there, because the Democrats will say things we can’t and won’t say about the government giving people things. Instead, we have to show we’re the party of success.”

Republican presidential candidate Marco Rubio discusses his father's story in a 60-second ad set to air in Iowa and New Hampshire. (Marco Rubio)

Cruz’s campaign is premised on the idea that it’s the conservative base, and especially evangelical Christian voters, who can put him over the top. Winning a larger share of the Hispanic vote would be nice, but the realistic upside isn’t high enough to make a difference in the outcome of the election, they believe.

To make his case about how misguided it is to focus on Hispanics as a separate voting group, Tyler likes to ask people what House Minority Leader Nancy Pelosi (D) and former New York mayor Rudolph W. Giuliani (R) have in common. Most people come up empty.

“They’re both Italian American, but people don’t get that at first,” Tyler said. “But there was a time when that would have been the first thing people noticed. Democrats don’t like it, but we’re approaching a time when you’ll say ‘Rodriguez and Gonzalez’ and nobody will see what they have in common until you remind them they’re both Hispanic.”

Carson, too, has criticized identity politics, calling the Black Lives Matter movement “sickening” and accusing its activists of “bullying people.”

Some party leaders worry that the GOP has painted itself into a tricky spot: The party can’t play the identity card because it would violate a core principle and turn off many of its most loyal voters. Yet identity plays an increasing role in a country in which California and Texas are already majority minority and many other states are moving in that direction.

“Obviously, Secretary Clinton’s focus on being the first woman was chosen because she thinks that will work,” said Sen. Tim Scott of South Carolina, the Senate’s only black Republican. “Rubio and Cruz can talk about how America provided opportunity for their families, but will that be enough? The election will tell us.”

Rep. Tom Cole (R-Okla.) says the high-profile presence of minority candidates at the top of early polls presents a “pivotal, transitional moment” for the party.

“Can we redefine ourselves, or do we have to lose a third straight election, like the Democrats did in the ’80s, before they redefined themselves?” Cole asked. “We have not done a good job of making people who feel as we do comfortable in our party. We have to change not what we believe but visually who we are. I take a great deal of pride in the political success of a Rubio, Cruz or Carson.”

Watts argues that ethnicity still matters. “Republicans claim they don’t play identity politics,” the former congressman said, “but my value to the party was they needed me on poverty issues. I have a party that doesn’t have a relationship with minorities. Ben Carson and Rubio and Cruz need to be talking about these groups and their issues. They need to be a bridge. Most of my white friends, I’ve been to their homes. But most of them have never been to my house. How can you as a party relate to me if you’ve never been in my world?”

Some Republican leaders believe the way to soften the Democrats’ hold on minorities is to field more black and Hispanic candidates and stay true to the party’s ideals.

“It’s obvious when one looks at the field on both sides which one is more reflective of America,” said Daniel Garza, director of the Libre Initiative. “But Ted and Marco are thriving because of their ideas, not their skin color. Yes, there are people who say, ‘See, we love Ben Carson and he’s black,’ but it’s his ideas that attracted them, not his skin color. The fact that they’re black or Latino is a bonus.”

Some Hispanic Republicans say the days of ethnic identity determining voting are waning. Immigration policy still drives many Hispanics’ votes, but that doesn’t necessarily translate into support for Hispanic candidates, said ­Alfonso Aguilar, director of the Latino Partnership for Conservative Principles, a Washington-based group that recruits Latinos into the conservative movement.

Aguilar, who hasn’t endorsed a candidate, said Hispanic conservatives looking for a path to citizenship for illegal immigrants “find Marco and Carson to be constructive, and we have a problem with Trump and with Cruz. But it’s not a matter of voting for someone who looks like them. It’s what they would actually do.”

Rodriguez’s experience with his workers in Iowa has convinced him that the rhetoric coming from some Republican candidates is more destructive than the ethnic identity of some of those candidates is helpful. “I can tell Latinos who work for me that ours is the moral party and the party for the church,” he said, “but they hear Trump and how he talks about us, and they hear how Cruz talks about immigrants, and they are driving people far from the party.”

But Alex Rios, a 30-year-old ad salesman in Des Moines who was born in Mexico and grew up in Los Angeles and Iowa, has settled on Cruz as his man in the February caucuses.

Rios doesn’t really agree with Cruz’s approach on immigration — Rios wants a clearer path to citizenship for people who arrived here illegally — but he says it’s time for Hispanic voters to make decisions based on bigger issues.

“People say to me, ‘No, man, don’t vote Republican, because the Democrats are going to help us with citizenship,’ ” Rios said, “but I don’t care about citizenship if we’re killing babies and destroying our Earth’s environment and making people dependent on government. There are more important things. I can’t get them to see that yet. They’re still thinking like Latino is more important than American.”