For several elections now, the Republican Party has done very poorly among American Hispanics. In the 2012 election they got less than 30% of the Hispanic vote, and their refusal to mitigate their policies regarding immigration reform and minority rights continues to hamper their efforts to appeal for support among Hispanics.
There has been one bright spot among Hispanic voters for the GOP -- the Cuban-American community. Because of the right-wing hatred for the Castro government in Cuba, and the right-wing support for special immigration rights for Cubans (with Cubans entering the country illegally being allowed to stay and become citizens, while Hispanics from other countries are deported), the Cuban community has traditionally been big supporters of the Republican Party.
However, that is now changing. Many younger Cubans (born and raised in this country) now support an end to the embargo of Cuba, and want the government to normalize relations with Cuba -- and they identify more with other Hispanic-Americans than their elders did. This is causing a significant shift in the political preferences in the Cuban community.
Back in 2002, about 64% of Cuban-American registered voters said they were Republicans (or leaned toward the GOP), while only 22% identified with the Democratic Party. But in the last decade or so there has been a radical change in political preference. Now only 47% identify as Republican, while 44% identify as Democrats (which is a 22 point growth for Democrats, and a 17 point drop for Republicans).
This should worry Republicans (especially in Florida, the state with the largest community of Cuban-Americans), because it means they are losing the only segment of the Hispanic community that they could count on to be reliable Republican voters. And it means their voter percentage among Hispanics (the fastest growing segment of the U.S. population) could be even lower in 2014 than it was in 2012.
The chart above was made from information provided by the Pew Research Center.