Latinos and others protest outside the GOP presidential debate in Simi Valley, Calif., on Sept. 16. (Robyn Beck/AFP/Getty Images)

Republican leaders are intensifying their outreach to Hispanics even as it has become increasingly clear that many within the party’s ranks are hostile to the idea — the clearest signal yet of how crucial Latino voters could be in 2016.

On Wednesday, Republican National Committee Chairman Reince Priebus met with Latino business and political leaders at a Mexican restaurant in Virginia. Two days earlier, former Florida governor Jeb Bush spoke to the U.S. Hispanic Chamber of Commerce in Houston.

While some Republicans are cheering Donald Trump’s promises to deport undocumented Latinos and his supporters’ chant “Press 1 for English,” Bush has promised to back immigration reform efforts to give millions of undocumented Latinos “a chance to earn legal status.” He also has showcased his fluent Spanish on the campaign trail to a degree never before seen in presidential politics. Sen. Marco Rubio (R-Fla.), another 2016 contender, has done the same.

Given demographic trends, some GOP leaders say such outreach strategies are essential to winning back the White House. But efforts to enlarge the GOP tent are complicated by the array of other Republicans sending dramatically different, even hostile, signals to Latinos and other minorities.

“We have to diversify. To do otherwise puts us in the dustbin,” said John Weaver, an adviser to Ohio Gov. John Kasich, who is also running for the GOP presidential nomination. “We have been in the wilderness on this issue for 10 years. The party has to grow with other groups or the math doesn’t work out.”

The math is hard to argue with: While white voters accounted for 83 percent of the electorate in 1982, that number dropped to 72 percent in 2012 — and is expected to continue to shrink. And that helps explain why, with their eyes on 2016, Republicans are paying new attention to Latinos, who will account for about 12 percent of eligible voters next year.

More than 800,000 Hispanics turn 18 every year and become newly eligible to vote. Critically, a growing number of them live in battleground states, including Virginia, that are considered vital to the GOP’s efforts to win the White House.

Attracting more Hispanic support is considered so important to the Libre Initiative, a conservative effort backed by the billionaire Koch brothers, that it is offering free services such as instruction in Spanish for U.S. driver’s tests.

And the RNC is now using bilingual staff members to help reach out to minority groups that “for too long we ignored,” said Jennifer Sevilla Korn, the party’s deputy political director and head of strategic initiatives.

“When you are talking about close elections and purple states, getting an extra 2, 3, or 4 percent is the difference between winning and losing,” Korn said.

Priebus’s appearance in Northern Virginia on Wednesday was one of two dozen events the RNC is hosting to celebrate Hispanic Heritage Month. He met with local Hispanic leaders surrounded by mariachi music and heaping plates of enchiladas at the El Paso Mexican restaurant. Afterward, he stood outside and promised that the GOP would be far more attentive to Latinos than it has been in the past. He spoke in front of an RNC sign that said, “Nuestro Poder,” or “Our Power,” and “Hispanic Roots, American Dreams.”

When asked by reporters about the starkly differing views within the party ranks on immigration and the use of Spanish, Priebus said, “There is no one opinion on any subject.” In the end, the party will pick a candidate that all will rally around, he said.

But these efforts will remain a hard sell with the bloc of Republican voters who have flocked to two presidential contenders known for their inflammatory rhetoric. In addition to Trump’s remarks, retired neurosurgeon Ben Carson got a boost from some conservatives this week when he said that he “absolutely would not agree” with a Muslim becoming president.

“Press 1 for English!” supporters of Trump shouted at Latino protesters outside his recent Dallas rally. In interviews, several lamented a bygone era, which they described as a time when the country attracted a blend of immigrants from various European countries who were forced to learn English to assimilate.

Now, said Peter Williams, a retired utility company employee from Fort Worth, there are so many Mexicans and Central Americans everywhere “that no one needs to bother to learn English.”

“The country is changing and not for the good,” he said. “We need someone to say, ‘Enough!’ ”

Gale Crawford, a Republican activist and retired banking executive in South Carolina, is part of the vocal party base that says it does not agree with a lot of things the “D.C. mafia” wing of the GOP says. She prefers Trump’s view.

Children are speaking Spanish in public schools, their parents are speaking it on the job, and now candidates are even speaking it on the road to the White House, she said. “It’s asking people to stay different,” she said.

“This is the United States of America and we speak English,” she said.

The efforts by party leaders to be more inclusive began after Mitt Romney’s decisive loss to President Obama in 2012. The RNC conducted an “autopsy,” and a major conclusion was that the party needs to reach out to Latinos and other minorities. Obama got only 4 out of 10 white votes, yet he won because of overwhelming support from other nonwhite groups.

But Crawford says that if all the like-minded Republicans go to the polls, their numbers are big enough — without support from minorities — to win back the White House.

Trump, to the delight of people such as Crawford, has chastised Bush for speaking Spanish, saying he “should set an example by speaking English in the United States.”

Mark Krikorian, executive director of the Center for Immigration Studies, said some of those in the ranks of the GOP feel “the elites have come to see themselves as citizens of the world, instead of Americans first.”

Bush and Rubio speaking Spanish as they run for president, Krikorian said, is seen “as a political statement” that some hear as: “Immigrants don’t have to conform to our ways. We have to adapt to them.”

Meanwhile Democrats, and Hillary Rodham Clinton in particular, are pumping more effort into Latino outreach than ever. Clinton has even started tweeting in Spanish.

Bush and Rubio, who have done extended interviews on Spanish-language networks, said they use the language as a sign of respect to audiences who speak it. Spanish is now the No. 2 language in the United States, with 38 million people older than 5 speaking it at home.

In Las Vegas last week, Sen. Rand Paul (R-Ky.) got into the mix. “Buenas noches,” he said, and he continued with a few more words in Spanish, asking the audience to forgive his “Spanglish.”

He later told reporters that Trump’s criticism of Bush’s Spanish language was “about the dumbest response I’ve ever heard from a presidential candidate.”

Jose A. DelReal contributed to this report.