A historic turnout by Hispanic voters helped fuel President Obama’s triumph in Tuesday’s election, with exit polls showing a growing share of Latinos casting ballots in a contest that has set off Republican soul-searching and left many Hispanic voters with a greater sense of political voice.

National exit polls showed that 10 percent of the electorate was Hispanic, compared with 9 percent in 2008 and 8 percent in 2004. Those numbers take on more significance when combined with results: Across the nation, 71 percent of Latinos voted for Obama, compared with 27 percent who chose Mitt Romney.

“This is a defining moment for the Republican Party,” said GOP strategist Leslie Sanchez. “If Republicans don’t heed this warning, we are certainly in danger of becoming politically irrelevant at a national level.”

Matt Barreto of Latino Decisions, a nonpartisan polling and research firm, said that in Nevada, Colorado and New Mexico, “Latino voters by themselves provided Obama with the margin of victory.” He also said the 2012 election shows that in key states — such as Ohio and Florida — a strong showing from Latinos and African Americans “in tandem” was a difference maker.

The Republican Party, he said, “will be doomed if they lose black and Latino votes by these same margins in the future.”

In many battleground states that were a key to winning the election, efforts to get Latinos registered and to the polls appear to have provided an edge for Obama.

The president himself was keenly aware of the importance of the Latino voting bloc before the election. “Should I win a second term,” Obama told the Des Moines Register last month, “a big reason I will win a second term is because the Republican nominee and the Republican Party have so alienated the fastest-growing demographic group in the country, the Latino community.”

The Hispanic vote undoubtedly helped Obama in Florida, where the Puerto Rican population in particular has boomed in recent years in the central part of the state, and where the president held a slight lead Wednesday as officials continued tallying votes.

Many of the new residents in places such as Osceola County — just south of Orlando — are Republicans who twice helped elect Jeb Bush as governor. But the area also went for Obama in 2008 and 2012. Perhaps most important, unlike many other Hispanic groups, Puerto Ricans are American citizens. They have no say in presidential elections back on the island, but in Florida, they are changing the electoral map.

“Here, we get to vote for president, and it matters. We have a voice,” chef Jesus Chevres, 53, said in his native Spanish on Wednesday, while preparing fried plantains and roast pork for the lunchtime crowd at the Broadway Restaurant in downtown Kissimmee.

The increase in Hispanic voting is a reflection of demographic changes, experts said, as non-
Hispanic whites account for a smaller share of the overall population. Exit polls showed 72 percent of voters were non-Hispanic whites, the lowest percentage since 1972.

“This is a reflection of the changing demographics of the country,” said Mark Hugo Lopez, associate director of the Pew Hispanic Center. “You see it at the state level and you see it nationally. Hispanics are a greater share of the electorate.”

For Pamela Guerra, a Denver Head Start teacher, the outpouring of Latino support for Obama felt similar to the passion black voters expressed four years ago. She described whole families going to vote and phone calls to distant cousins. “That’s how Latinos can operate,” she said, speaking above the whoops of a Democratic celebration at a downtown hotel shortly after Obama’s victory speech. “We finally found our voice.”

The spark was clear, she said: A growing perception of hostility toward illegal immigrants by Republican candidates is driving many Latinos to the polls.

“It’s the tone,” said Guerra, 49. “It’s like a hatred.”

Her daughter Fransheska, 20, a psychology student at the University of Denver, said many of her young friends were motivated to vote by a fear of conservative attacks.

“When you’re silent, this is what you’re going to get,” she said. “Everybody was really adamant about participating this year.”

Sanchez, the Republican strategist, who wrote the book “Los Republicanos: Why Hispanics and Republicans Need Each Other,” said Democrats have succeeded in defining Republicans as uncaring toward Latinos. Romney, she added, failed to articulate “a compassionate and realistic approach” on immigration reform and the Dream Act. He also misstepped in speaking of “self-
deportation” as a way to address illegal immigration, she said.

The push in 2012 to get Latinos registered and voting was months in the making, said Ben Monterroso, national executive director of the nonpartisan La Familia Vota, which had 600 people in six states registering more than 80,000 voters. In Florida and Nevada, the group exceeded its goal of increasing registration by 10 percent among those eligible to vote, he said. In Colorado, it came close.

“I believe the Latino vote made the difference,” he said. Now, he said, he expects political leaders to listen. The election’s message, he said, was, “Here we are, and you need to deal with our issues and treat us with respect.”

The top issues for Latino voters, he said, are the economy and jobs, immigration reform, education and health care.

On Wednesday, in the heart of the Hispanic community of Las Vegas, where Obama campaign signs in Spanish were posted down the street from a Romney field office, Jose Flores, a 23-year-old electrician and Obama supporter, recalled cheering the television as voting results rolled in the evening before.

“I think the next four years will be good,” Flores said.

Dennis reported from Kissimmee. Steve Hendrix in Denver and Julie Tate in Washington contributed to this report.