Leading Republicans, from Karl Rove to Florida Sen. Marco Rubio, see the passage of the U.S. Senate's immigration bill as necessary for future GOP success with Hispanics, a fast-growing portion of the electorate that has voted strongly Democratic in recent years. But past and ongoing opposition to an immigration overhaul may have already done too much damage to the GOP "brand."

To gauge how big a hole the party is in with Hispanics, we looked at states and legislative districts that are home to a significant number of Hispanics, scrutinizing whether GOP candidates have had any success winning over Hispanic voters.

According to interviews with national and state political observers, it remains rare for Hispanic Republicans to win either statewide or state legislative offices in predominantly Republican states or districts. This isn't to say that Hispanic Republicans aren't winning office -- they are. But when they win, it's most often due to the support of non-Hispanic voters who share their conservative ideology. It remains quite rare for Hispanic Republicans to actually win a large share of votes from Hispanic voters. (The main exceptions are Cuban-American lawmakers in Florida, including Rubio.)

Nationally, Hispanic voters' strong and growing preference for Democratic candidates is no secret. In 2004, Democratic presidential nominee John Kerry won 58 percent of the Latino vote. In 2008, Barack Obama won 67 percent, and four years later, Obama won 71 percent.

Since then, the ongoing battle over immigration reform -- in which a bill that passed the Senate sits stalled, perhaps fatally, in the GOP-controlled House -- has only worsened the challenges for Republicans who want to expand the party's reach among Hispanics.

A July survey of 600 Latino voters asked which party would deserve the blame if immigration legislation does not pass; 69 percent said the Republicans, compared to 13 percent who said the Democrats. The poll was conducted by Latino Decisions and Hart Research, a Democratic firm, and was sponsored by the Service Employees International Union, which leans Democratic.

The same poll found that only 29 percent of Latinos believed the Republican Party "respects the Latino community," compared to 67 percent who said the GOP did not respect the Latino community.

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In Congress, there's little overlap between the roster of Republican lawmakers with Hispanic ancestry on the one hand, and heavily Hispanic districts on the other. The nonpartisan Cook Political Report determined that in the current House of Representatives, just 24 Republicans represent a district in which Hispanics make up at least 25 percent of the population. Most of these districts are strongly Republican; all but four supported GOP nominee Mitt Romney in the 2012 election, by margins of two to 60 points. And all but two of the lawmakers representing these districts are Anglo. The only exceptions are a pair of Cuban-American lawmakers from South Florida -- Mario Diaz-Balart and Ileana Ros-Lehtinen.

By contrast, other Hispanic Republicans in Congress -- including Bill Flores of Texas, Jamie Herrera of Washington state and Raul Labrador of Idaho -- represent safely Republican districts with a smaller percentage of Hispanic voters.

In the Senate, the only Hispanic Republican currently serving other than Rubio -- Ted Cruz of Texas -- appears to have done a few percentage points better than Mitt Romney among Hispanic voters in 2012. But even so, Cruz still lost Hispanics in that same election by a two-to-one margin.

The picture for the GOP isn't much brighter in state-level offices.

One Hispanic Republican who's attracted attention -- and who is enough of a comer to be forming an exploratory committee to run for secretary of state -- is Arizona state Rep. Steve Montenegro.

Born in El Salvador, Montenegro has taken staunchly conservative positions on immigration, appearing with hardliners such as Maricopa County Sheriff Joe Arpaio and former state Sen. Russell Pearce. Such positions have won him prominence in Republican circles but few friends among Latino voters.

Montenegro's district is 38 percent Hispanic, which is higher than the state average of about 30 percent. But there's no indication that Latino voters are warming to his platform. "If Montenegro wins, it won't be because of Hispanics, and he knows it," said Stephen Nuno, a Northern Arizona University political scientist. "He has risen through the party specifically because of his surname and his willingness to co-sponsor anti-immigrant bills."

In Texas, another Hispanic Republican rising star, state Rep. Jason Villalba, a member of Mitt Romney's National Hispanic Steering Committee in 2008, represents a Dallas-area district that's affluent, predominantly white, solidly Republican and just 7.5 percent Hispanic. Villalba told D Magazine that in his district, "there are 482 registered Hispanic Republicans. Out of 93,000."

"Texas Latino Republicans win in the same kinds of districts where white Republicans win -- places with minimal political challenge from Democrats, which covers a whole lot of state and local offices, and places with relatively low minority voter participation," said Sylvia Manzano, a senior analyst with Latino Decisions.

In Colorado, freshman Republican state Rep. Clarice Navarro represents Pueblo, a city with a sizable Hispanic population near where she was raised by a single mother. Navarro had to walk a tightrope between her constituents and her party earlier this year, when she became one of just a handful of Republican legislators to support a bill that provided illegal immigrants with in-state college tuition rates.

In Colorado, said Denver-based independent pollster Floyd Ciruli, Navarro and other Hispanic Republicans will have to work hard to overcome the GOP's image, which in recent years has been symbolized by Tom Tancredo, a former member of Congress and leading opponent of loosening immigration laws. "Until Tancredo moves on or is crushed in the primary or general," Ciruli said, "it's hard to see Colorado Republicans making credible or effective overtures to Hispanic voters."

But the biggest electoral wasteland for Hispanic Republicans is California, where the anti-immigrant Proposition 187 in 1994 was a political earthquake -- one that continues to reverberate. "The GOP has no statewide officeholders, no Latino members of Congress and only two Latinos in the entire 120-member legislature, both of them freshmen," said California Democratic strategist Garry South.

In a Los Angeles Times column published earlier this year, South rattled off a series of grim statistics for California Hispanic Republicans. "In three of the last four non-presidential elections," South wrote, "Republicans actually nominated Latinos for statewide office: Ruben Barrales for controller in 1998, Gary Mendoza for insurance commissioner in 2002 and Maldonado for lieutenant governor in 2010. All three were attractive, articulate candidates with compelling personal stories. But all three went down in flames, receiving an average of only 37.9 percent of the vote. And there is no indication in post-election analyses that they received any meaningfully higher share of the Latino vote than a white male GOP candidate would have gotten."

The outlook is no brighter for 2014: Former appointed Lt. Gov. Abel Maldonado may run against Democratic Gov. Jerry Brown, but if he wins the nomination, he would be a decided underdog against Brown.

Two Hispanic rising stars with appeal for Republicans are a pair of governors elected in 2010: Brian Sandoval of Nevada and Susanna Martinez of New Mexico. They were elected in states with Hispanic populations of 27 percent (Sandoval) and 46 percent (Martinez). But polling suggests that neither won office with anything close to a majority of the Hispanic vote.

Politico recently noted that Sandoval won just one-third of the Latino vote in 2010, according to CNN exit polls, while a Latino Decisions poll taken the night before the election found that 38 percent of Latinos said they would be supporting Martinez. The positive news for the GOP is that both have since improved their standing among Hispanic voters -- and both look like safe bets for re-election in 2014. To make inroads, they have each staked out more moderate positions on immigration than they had during their initial gubernatorial campaigns.

Sandoval backtracked from his prior support for Arizona's S.B. 1070, endorsing the U.S. Senate version of the immigration bill. Martinez, for her part, has spoken favorably of the U.S. Senate bill, though she expressed a preference for a pathway to legal status rather than full citizenship for illegal immigrants. She has also sought to overturn a state law that allows illegal immigrants to secure driver's licenses. (Some say the deeply rooted Hispanics of New Mexico, many of whose families predated white settlement, are more tolerant of laws that tighten immigration controls.)

Another Hispanic elected official in New Mexico, Secretary of State Dianna J. Duran, has faced a similar tightrope walk. Elected in 2010 alongside Martinez following a series of Democratic ethical scandals, Duran has attracted criticism from Democrats and others for taking aim at alleged voter fraud in the state. That's an issue that has prompted fierce battles in many states between Republicans, who are seeking stricter election rules, and Democrats, who say that the potential for disenfranchising poor and minority voters outweighs any problems with voting fraud.

The one bright spot for Republicans seeking to expand the party's Hispanic support is South Florida, where Cuban-American voters have historically voted Republican. This affinity has roots in the anti-communist leanings of early generations of Cuban immigrants who fled Fidel Castro.

While more recent generations of Cuban-Americans are increasingly open to voting Democratic, 10 Hispanic Republicans continue to serve in the Florida House, along with three Hispanic Republicans in the state Senate. All are from South Florida districts, mostly from Miami-Dade County. "These are Cubans representing relatively safe, Cuban-majority districts," said Aubrey Jewett, a political scientist at the University of Central Florida. "So they do not feel as much pressure from Anglo Tea Party Republicans and social conservatives."

Ana Navarro, a Hispanic woman and Republican strategist in Coral Gables, Fla., agreed. These legislators win Hispanic votes "by staying away from D.C. battles and keeping it local," she said. "Their outreach, their focus on issues and their press is all local, and they have no qualms about opposing some federal Republicans when they have to, like on immigration issues."

An example of flexibility on immigration policy within the Florida GOP came on a bill that would have helped give temporary driver's licenses to children of illegal immigrants who attend school in Florida. The measure easily passed both Republican-controlled chambers of the legislature, though it was later vetoed by GOP Gov. Rick Scott.

Such episodes suggest that moderation on immigration can strengthen Republicans' electoral chances. "The Hispanic Republicans in Florida are more moderate than other Republicans, especially those from the Panhandle," said Steven Tauber, a University of South Florida political scientist. Whether that is a model that Republicans choose to pursue outside of South Florida -- and whether Hispanic voters respond favorably if they do -- remains uncertain.