From the convention stage here, the Republican Party has tried to highlight its diversity, giving prime speaking slots to Latinos and blacks who have emphasized their party’s economic appeal to all Americans.

But they have delivered those speeches to a convention hall filled overwhelmingly with white faces, an awkward contrast that has been made more uncomfortable this week by a series of racial headaches that have intruded on the party’s efforts to project a new level of inclusiveness.

The tensions come amid a debate within the GOP on how best to lure new voters. The nation’s shifting demographics have caused some Republican leaders to worry not only about the party’s future but about winning in November, particularly in key swing states such as Virginia and Nevada.

“The demographics race we’re losing badly,” said Sen. Lindsey O. Graham (S.C.). “We’re not generating enough angry white guys to stay in business for the long term.”

On Tuesday, convention organizers ejected two attendees after they reportedly threw peanuts at a black CNN camerawoman and told her, “This is how we feed animals.” Organizers called the conduct “inexcusable and unacceptable.”

That followed an on-air shouting match between MSNBC host Chris Matthews and Republican National Committee Chairman Reince Priebus over whether presidential nominee Mitt Romney was injecting race into the campaign by joking about President Obama’s birth certificate and attacking his record on welfare reform.

“There’s no doubt he did,” Matthews declared.

“Garbage,” Priebus retorted.

And on Wednesday, Yahoo News fired Washington bureau chief David Chalian after a live microphone caught him telling a colleague, before an online event, that Romney and his wife, Ann, were “happy to have a party with black people drowning,” a reference to the RNC’s decision to go ahead with the convention while Hurricane Isaac lashed New Orleans. Chalian later apologized.

By early Wednesday, the conservative Drudge Report featured a block of headlines devoted to issues of race at the convention, most of them critical of liberal news outlets that didn’t air speeches by the GOP’s diverse lineup.

Not all of the race talk has been of the party’s own making. Many Republicans argue that Democrats’ obsession with the issue has forced it to the forefront. They say Democrats have used overtly racial appeals to fire up their base, citing Vice President Biden’s recent charge at a Virginia campaign event attended by hundreds of black voters that the GOP’s approach to financial regulation would“put y’all back in chains.”

Still, the discussions of race this week have highlighted the Republican Party’s continued difficulty in attracting non-white supporters.

Exit polls from 2008 showed that 90 percent of GOP voters were white, a homogeneity that has been consistent for more than 30 years, even as the percentage of the electorate that is white has fallen.

Nonwhite voters favored Obama over Romney by better than three to one in a Washington Post-Kaiser Family Foundation poll from early August; 74 percent of Latino voters and 90 percent of African Americans backed Obama.

And despite a speaker lineup in Tampa that includes Artur Davis, a black former Democratic congressman; former secretary of state Condoleezza Rice; and Utah congressional candidate Mia Love, who would be the party’s first black congresswoman if she won in November, just 2 percent of convention delegates are black.

That’s according to an analysis by David Bositis of the Joint Center for Political and Economic Studies. Bositis also said that only two members of the 165-member RNC are black and that none of the leaders of the committees responsible for drafting the GOP platform and adopting the convention rules are black.

“This Republican Party base is white, aging and dying off,” he said.

Many Republicans, however, worry about making overt racial appeals to minorities.

“Amongst politicians, amongst people who cover politics, there’s an overwhelming tendency to silo voters,” said Wisconsin Gov. Scott Walker at a breakfast hosted by The Post and Bloomberg News. “As Republicans, we take on a huge risk if we try to appeal to voters . . . within a mind-set of silos instead of making direct appeals on the issues that they’re actually talking about in their household — not necessarily in their category, but in their household.”

A new Post poll put the difference between the two parties’ perception of minority voters on stark display. Respondents were asked an open-ended question: Why do most black voters so consistently support Democrats?

Though “don’t know” was the top answer for members of both parties, a close second among Republicans was that black voters are dependent on government or seeking a government handout. Democrats more often said that their party addresses issues of poverty.

In Tampa, Republicans have devoted significant time to brainstorming how to expand the party’s appeal to Latinos. At various forums and lectures, they have debated whether the GOP should change its tone in discussing illegal immigration, appeal more directly to religious Latinos on social issues or make a more explicit argument that Republicans can help boost the economic prospects of Latino communities.

“We as a party have got to get it,” said Mel Martinez, a former senator from Florida and a former RNC chairman, speaking at a Tuesday event sponsored by Univision and the National Journal. “We’ve got to get smart about this. We could be relegated to a minority party. . . . We’ve got to find a way to make that connection.”

There has been less discussion of new ways to reach out to black voters, in part out of a recognition that the first African American president has a special relationship with African American voters.

Davis, who in 2008 helped nominate Obama at the Democratic National Convention but became disenchanted with the president’s handling of the economy, said that to reach black voters, Republicans must expand their message beyond limiting government.

“It’s not just enough to go into the black community and say, ‘We want to keep government from taking over your life.’ That doesn’t resonate in a whole lot of the black community, who have come to see government as a salvation and as economic leveler,” he said. “It’s going to take being willing to define conservatism as not just a defense of economic liberty but as a broader way of constructing a society that can promote social mobility.”

Romney adviser Tara Wall said, “We know that a majority of black Americans will vote for President Obama,” but “that doesn’t mean Democrats or President Obama own the black vote or can take every black vote for granted.”

She said Romney’s policies on school choice, social issues and job creation appeal to black families.

“These are some common principles that we share and that we can engage on,” she said. “This is a long-term effort. It doesn’t happen overnight.”

Raynard Jackson, a black GOP political consultant, wrote Tuesday on the RootDC Live blog that he is “embarrassed by the lack of diversity” at the convention and frustrated by his party’s empty promises.

“The Republican line is that the overwhelming majority of blacks will vote for Obama because he is African American,” Jackson wrote. “I find this thinking extremely insulting as a black Republican. The reason the majority of blacks will vote for Obama is because Republicans have not given African Americans a reason to vote for Republicans or Romney.”

Aaron Blake contributed to this report.