Earlier this month, nearly a hundred of the wealthiest Republicans in the country gathered at the home of Woody Johnson, the owner of the New York Jets and an heir to the Johnson & Johnson pharmaceutical family, for a GOP fundraiser. The crowd was nearly all white, and older, and male (“There was one Native American guy there, I think,” said one attendee) and sat at two long tables in overlooking Fifth Avenue in Manhattan in the $75 million duplex’s drawing room.

A number of top would-be contenders to the GOP presidential nomination, including Florida Sen. Marco Rubio, Ohio Gov. John Kasich, and even Mitt Romney, were there to make their pitch to the assembled masters of the universe. So were two of the early polling leaders of the long presidential contest—Gov. Chris Christie of New Jersey and Sen. Rand Paul of Kentucky.

And what both Paul and Christie spoke about, according to sources in the room, was how popular they were among those who are as far away from Fifth Avenue drawing rooms as you can get: poor, black, and Hispanic voters who, when they vote at all, almost reflexively vote Democratic.

Telling some of the wealthiest Americans to give you money because of how well-loved you are by some of the nation’s poorest people struck some of those in attendance for its incongruity; but equally interesting was how Christie and Paul seemed to be boxing one another out over who is best able to carry the Republican banner into America’s inner cities.

The notion of the GOP expanding its universe of potential voters has been on the party’s agenda since Romney lost the 2012 presidential election, largely, party brass figured, by not broadening their appeal to the so-called Obama coalition: blacks, Hispanics, women, and young people. In 2012, Romney won about 60 percent of the white vote—an amount that would have given him a victory back in 1992, when 87 percent of the electorate was white. In 2012 though, white voters accounted for just 72 percent of the electorate, and so only getting six out of every 10 of them spelled doom. After the election, a team of Republican pooh-bahs gathered to figure out how to fix the party’s weaknesses. Among the efforts they recommended: a $10 million outreach effort to minority communities.

“If we want ethnic minority voters to support Republicans, we have to engage them, and show our sincerity,” reads one of the report’s 219 recommendations.

No one seems to have taken this message to heart quite as much as Paul, who has made it a point since 2012 to travel to the kinds of places Republicans don’t usually go, like historically black colleges, inner-city churches, and, over the summer, to the Urban League, where he spoke of his support for restoring voting rights for felons and outlined a proposal to bring “Economic Freedom Zones” to poor neighborhoods.

But Christie seems unwilling to cede this ground to Paul. He’s called for sentencing reforms for those arrested on drug charges, has made it a point to visit hard-hit Jersey cities like Camden, and last week spoke at the New Jersey NAACP’s annual membership event, where he talked up his efforts at bail reform and for making it easier for ex-offenders to seek employment.

At the penthouse fundraiser, according to sources who were in the room, Christie made his case for why he would be the best candidate to expand the GOP’s base (without mentioning Paul) by pointing out his record in New Jersey. In 2013, Christie grabbed 21 percent of the black vote and captured a bit more than half of the Hispanic vote.

To the Paul camp, Christie is a late arrival to an issue they already own. They see the governor’s numbers in 2013 among minorities as more of a function of weak opposition than any appeal that Christie made (Christie did in fact improve his numbers among black voters at nearly precisely the rate he improved on his overall vote totals from 2009—12 percentage points.)

To Christie supporters, Paul is just trying to distance himself from some of the more unsavory aspects of his career, and that of his father, Ron Paul, including ties that the former congressman and erstwhile presidential candidate had to segregationists. Paul dug himself a hole in this regard when he expressed disapproval of the Civil Rights Act as a Senate candidate in 2010 and for hiring a pro-segregationist former radio host as a top aide. Plus, Christie advisers point out, Paul merely talks about the reforms that the governor has implemented.

Glenn McCall, an African-American national GOP committeeman from South Carolina who helped draft the party’s post-November post-mortem, said that he was pleased with the progress Republicans had made so far in reaching out to diverse constituencies. When asked who in particular he liked, McCall immediately named Paul.

“I think Rand Paul has definitely demonstrated that he is taking his message to all communities and especially ethnic communities and historically black communities.”

But in the same breath, he added, “I also look at the work that Chris Christie has done in New Jersey.”

Obama won 93 percent of the black vote in 2012, a figure that GOP strategists say they do not think a white Democrat would be able to match in 2016. But still, supporters of both Paul and Christie say that the pitch to African Americans is not necessarily a plan to attract African-American voters; it is to signal to white, suburban and centrist voters who view the Republican Party through the lens of its anti-civil-rights past that it is OK to vote GOP.

Either way, this is a conversation that is occurring not just at the penthouse level, but among the grassroots as well. Rank-and-file conservatives who are trying to draft former Congressman Allen West or surgeon Ben Carson into the race say that they believe either would can appeal to black voters in a way that white Republicans cannot.

“With the right campaign, [Carson] can get 17 percent of the black vote,” Vernon Robinson, a conservative activist from North Carolina who is trying to draft the doctor into the race, told The Daily Beast in July. “The problem for the left is their normal demonization tactics won’t work. There are a whole generation of black folk who wanted their sons to be Dr. Carson, and their daughters to marry him. It will be a huge problem for them to demonize the guy.”

And there are still some in the Republican Party who think all of this outreach is a mistake.

“You have to be realistic. We are not going to get 50 percent of the African-American vote,” said John Brabender, an adviser to Rick Santorum’s 2012 presidential campaign. He said he thinks that the party would be better served by sharpening its message to low- and moderate-income voters of all races.

“It is dangerous if you segment the population with your messages. It looks like you have no core conviction.”