WASHINGTON -- Latinos helped deliver President Barack Obama’s re-election Tuesday with near-historic support. In return, they’re demanding an immigration overhaul and are warning both parties, particularly Republicans, that it’s time to get on board and pay closer attention to their issues.

Latinos accounted for 10 percent of those who voted Tuesday. They backed Obama with 71 percent of their vote nationally, compared with Mitt Romney’s 27 percent, according to exit polls. It was the highest level of Latino support since President Bill Clinton received 72 percent of their vote in 1996.

Obama arguably won the election in part because of Latino support in the swing states of Colorado, where he carried 75 percent of Latino votes, and Nevada, where he received 70 percent.

“Latino voters confirmed unequivocally that the road to the White House goes through Hispanic neighborhoods,” said Clarissa Martinez, the director of civic engagement and immigration at the National Council of La Raza, a Hispanic advocacy organization.

Activists such as Martinez think the election is such a game-changer for Latino issues that Republicans have no choice but to return to the negotiating table and confront the immigration problem.

Latinos are the country’s fastest-growing minority bloc. Seventeen percent of eligible Latino voters live in battleground states. Nearly 900,000 eligible Latino voters turn 18 each year.

Knowing those numbers, and even before Obama was named the victor Tuesday night, Republican strategists were calling for a new approach.

“I said this in the spring. In the summer. Biggest mistake was going hard right on immigration. Paying price,” John Weaver, a Republican strategist who worked on the presidential campaigns of Sen. John McCain and former Utah Gov. Jon Huntsman, tweeted about Mitt Romney.

Attention has turned toward rising Republican star Sen. Marco Rubio of Florida, who could serve as the catalyst to bring the sides together. The son of Cuban immigrants, Rubio said earlier this year that he was working on a compromise on the DREAM Act for young undocumented immigrants brought here illegally by their parents.

On Wednesday, he said “Republicans need to work harder than ever” on immigration issues.

Romney seemed to telegraph his predicament last spring. In the same fundraising-dinner video now infamous for his “47 percent” statement, he says trying to attract Hispanic voters is the party’s greatest challenge.

“If the Hispanic voting bloc becomes as committed to the Democrats as the African-American voting bloc has in the past, well, we’re in trouble as a party and, I think, as a nation,” he says in the secretly recorded video.

Yet during the primaries Romney called for a “self-deportation” program and picked one of the authors of Arizona’s controversial immigration law as an adviser. Obama, meanwhile, used his executive powers to grant two-year deferrals to hundreds of thousands of young undocumented immigrants.

There’s no question that Republicans lost votes because of their hard-line stance, said Gary Segura, a Stanford University political science professor who runs Latino Decisions polling. Some 60 percent of Latino voters know someone who’s living in the country illegally, according to the polling.