Republicans who are eager to repair the party’s battered image among Hispanic voters and unseat President Obama next year have long promoted a single-barrel solution to their two-pronged problem: putting Sen. Marco Rubio on the national ticket.

The charismatic Cuban American lawmaker from Florida, the theory goes, could prompt Hispanics to consider supporting the GOP ticket — even after a primary contest in which dust-ups over illegal immigration have left some conservative Hispanics uneasy.

But Rubio’s role in recent controversies, including a dispute with the country’s biggest Spanish-language television network and new revelations that he had mischaracterized his family’s immigrant story, shows that any GOP bet on his national appeal could be risky.

Democrats had already questioned whether a Cuban American who has voiced conservative views on immigration and opposed the historic Supreme Court nomination of Sonia Sotomayor, the first Latina justice, could appeal to a national Hispanic electorate of which Cubans are just a tiny fraction but have special immigration status. And Rubio’s support in Florida among non-Cuban Hispanics has been far less pronounced than among his fellow Cubans.

That ethnic calculus was further complicated by records, reported by The Washington Post last week, showing that Rubio had incorrectly portrayed his parents as exiles who fled Cuba after the rise of Fidel Castro. In fact, their experience more closely resembles that of millions of non-Cuban immigrants: They entered the United States 21 / 2 years before Castro’s ascent for apparent economic reasons.

Rubio made the exile story a central theme of his political biography, telling one audience during his Senate campaign, “Nothing against immigrants, but my parents are exiles.” A video, apparently produced for the conservative site, shows black-and-white footage of Castro as Rubio speaks.

Even after the new reports of his parents’ entry, Rubio has said he remains the “son of exiles,” saying his parents had hoped to return to the island but did not because of the rise of a communist state.

But in elevating exile roots over the apparent reality of his parents’ more conventional exodus, Rubio risks setting up a tension point with the country’s Hispanic voters — most of whom are Mexican American and have immigrant friends or ancestors who did not have access to the virtually instant legal status now granted to Cubans who make it into the United States.

“If he does take that mantle, there’ll be a lot of clarification that he’ll have to make on a whole lot of issues,” said Lionel Sosa, a longtime GOP strategist.

Hispanic voters are growing in importance and are expected to play a pivotal role in deciding who wins the important presidential battlegrounds of Colorado, Nevada, New Mexico, Arizona and Florida. Obama won two-thirds of the Latino vote in 2008, signaling a shift away from the GOP since 2004, when President George W. Bush won about 40 percent — an unusually high showing among Hispanics for a Republican.

GOP strategists see an opening in Obama’s sagging approval ratings and frustration among Latinos over the administration’s stepped-up deportations of illegal immigrants. But they worry that window is closing amid sharp rhetoric in recent weeks from the party’s apparent presidential front-runner, former Massachusetts governor Mitt Romney, who has accused Texas Gov. Rick Perry, his chief rival, of being soft on illegal immigration for his support of in-state college tuition for many immigrant children. Romney used a similar tactic in his 2008 presidential campaign, attacking Sen. John McCain (Ariz.) from the right on immigration.

Adding to those concerns is a Rubio-related standoff between the top Republican candidates and Univision, a Spanish-language TV network based in South Florida whose news programs draw more viewers in many cities than English-language broadcasts.

The candidates are refusing to participate in a potential Univision debate slated for Jan. 29, two days before Florida’s primary, citing a dispute between network executives and Rubio’s office over a July report on the 1987 drug-trafficking arrest of Rubio’s brother-in-law.

Rubio’s office said it was a “tabloid” story and unsuccessfully pushed for Univision executives to kill it. Two months later, a Miami Herald report cited unnamed network staff members and Rubio’s office accusing Univision of a quid pro quo, offering to soften or kill the story in exchange for Rubio agreeing to appear on the network’s Sunday public affairs show “Al Punto.”

Univision denied the charge. But after the report, a group of Rubio allies called on the GOP candidates to boycott the debate. The top candidates agreed, meaning they will be spared a potential grilling on immigration by the network’s high-profile anchor, Jorge Ramos, an advocate for more liberal immigration laws.

But the dispute creates ill will between Rubio, who could become the most powerful Hispanic political figure in the country, and one of the most cherished Hispanic institutions in the United States — and one that happens to be based in his home town.

“One of the big questions of 2012 is whether putting Marco Rubio on the ticket can help the GOP make up lost ground with Latino voters,” said Simon Rosenberg, president of the pro-Democratic group NDN, which analyzes the Hispanic vote. “Despite being Hispanic, looking at his overall record . . . he seems remarkably ill-suited to be the one reaching out to the largely Mexican migrant community in the key battleground states.”

Several Hispanic Republicans and other experts on Latino politics said in interviews that Rubio remains a potent force in the GOP. His presence on the party’s ticket could inspire enough ethnic pride to make up for cultural or policy differences. But they said there is no guarantee.

“He would deliver Florida,” home to the large and typically Republican-leaning Cuban American population, said Alfonso Aguilar, executive director of the Latino Partnership for Conservative Principles, a pro-GOP group that is planning to air ads in Western states geared toward Hispanic voters. “In Colorado, Nevada and New Mexico, he can have an impact. But can he deliver the Latino vote in those states? No.”

Some Republicans consider Rubio such a promising new star that they funded a poll last month that tested, among other things, the senator’s image among Hispanic voters in key presidential battlegrounds. The survey, by the group Resurgent Republic, found that most Hispanic voters outside Rubio’s home state aren’t familiar enough with him to express a view. But in Florida, it showed mixed results — with Obama viewed slightly more favorably than Rubio among Hispanics and the senator viewed favorably by just 42 percent of non-Cuban Hispanics.

Democrats predict that the numbers for Rubio would drop fast once more voters learned his views. Rubio’s allies say the survey shows that he could boost a party whose support among Latinos is sinking but that could probably win the presidency with just 40 percent of that electorate.

“Most Republican politicians would die for” his favorability rating among non-Cuban Hispanics, said Whit Ayers, the GOP pollster behind the survey, who worked for Rubio’s campaign in 2010.

Rubio has said he does not want to run for vice president. His spokesman, Alex Conant, declined to address that speculation. Instead, he reiterated the senator’s embrace of his heritage and his support for legal immigration.

“Sen. Rubio has always claimed to be both the son of immigrants and the son of exiles,” Conant said in an e-mail. “His family came to the country legally with the intention of staying permanently, but with the hope of someday returning to their homeland. They were unable to do that because of Castro, becoming exiles like many other Cuban-Americans.”


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