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“I still get some questions about it, mostly out of curiosity, not really because people think it’s weird,” he said. “I think in the last five to 10 years you’re seeing more and more Hispanic-American figures that are running for national office, or state office, as Republicans.”

The “Hispanic” label can get blurry at times. Mr. Flores’ family has lived in the United States longer than most, immigrating to Texas from Spain in 1725.

“I consider myself an American before I consider anything else,” said the ninth-generation Texan. “I can’t help who I am … I am proud of my background, proud of my heritage, but I never made a big deal out of it.”

Bill Schneider, a political expert with Third Way, a centrist Washington think tank, said the success of Hispanic Republican candidates this year doesn’t represent a significant long-term trend. Rather, their victories - like those of all GOP candidates - were tied mostly to the GOP’s success in capitalizing in voter angst over the economy and a desire for change in Washington.

The growing influence within the Republican Party of the “tea party” movement - and its often anti-immigration rhetoric - isn’t helping the party attract Hispanics, he added.

“The problem is Latinos still don’t trust Republicans,” Mr. Schneider said. “And whatever outreach efforts Republicans have made their criticism of illegal immigration does come across often as shrill … and that just creates a very difficult barrier.”

AEI’s Mr. Ornstein agrees that immigration issues pose hurdles for the GOP’s recruitment of Hispanic candidates.

“There has been a radioactivity to the Republican Party [with Hispanics] because of some of the harsh rhetoric on immigration, and that includes policies that hit at legal resident aliens for awhile as well as illegals,” he said. “It’s like [saying] ‘we don’t want your kind here.’ “

But many Hispanic Republican candidates are comfortable holding strong anti-illegal immigration positions. Mr. Labrador and Mr. Flores, who easily won their races, based their campaigns in part on strengthening the U.S. borders’ against illegal immigration.

And while Mr. Rubio last spring said he had “concerns” about Arizona’s tough new immigration law, he later criticized the Justice Department’s lawsuit over the policies as a “waste of resources.”