By Jose Serrano (staff@latinospost.com) | First Posted: Dec 19, 2015 11:10 AM EST

(Photo : Justin Sullivan / Staff Getty Images )

In 2013, Florida Sen. Marco Rubio joined Democrats in supporting an immigration reform bill allowing undocumented immigrants a pathway to citizenship. In the same year, Texas Sen. Ted Cruz introduced various amendments aimed at closing that path while opening some towards legal status.

Cruz and Rubio - today the second and third-placing Republican presidential candidates in most national polls - have trouble distancing themselves from those decisions, mainly because the other consistently brings it up on the campaign trail and during GOP debates.

Both are first-generation Cuban-American candidates. Both are in their mid-40s. Both represent Latino-heavy states. Yet, both adamantly oppose amnesty for undocumented individuals.

Tuesday's Republican debate in Las Vegas was the more recent skirmish between the two. Cruz badgered Rubio for supporting the 2013 bill, noting that both President Obama and New York Sen. Chuck Schumer endorsed similar legislation.

"Securing our borders and stopping illegal immigration is a matter of national security. That's why I fought so hard to defeat President Obama and the Republican establishment's Gang of 8 amnesty plan," Cruz said. "Their misguided plan would have given Obama the authority to admit Syrian refugees, including ISIS terrorists. That's just wrong."

Rubio fired back by referencing Cruz's plan, which would have given undocumented immigrants legal standing in the U.S., albeit without voting rights.

"He supports legalization, and I think his hope was once he got into the general election, to then start talking about legalization as a way to attract more voters," Rubio said.

Cruz and Rubio campaigns run averse to Donald Trump's; one openly proposing mass deportation and a ban on all Muslims entering the country. To win the nomination, they may have to completely abandon their Hispanic background.

A Public Policy Polling report taken after Tuesday's GOP debate shows Trump remains the clear leader, garnering 34 percent of the vote. Cruz came in second with 18 percent and Rubio followed with 13 percent, respectively.

More than half - 54 percent - were open to the idea of shutting down Mosques, and the same amount supported Trump's proposal of stopping Muslims from coming to America.

If the Party's nomination came down to Cruz and Rubio, the Texas senator would win by a 48 to 34-point margin. Fifty-four percent believed Cruz was more conservative than Rubio on pertinent issues.

The reason may be in Cruz's hardline stance on national security issues, specifically immigration and how he plans on handling some 11 million undocumented individuals living on U.S. soil. He seldom acknowledges his Latino heritage, and often uses the term "illegal" rather than "undocumented," as he did at a Nevada campaign stop on Thursday.

"I oppose amnesty. I oppose citizenship. I oppose legalization for illegal aliens," Cruz said. "I always have, and I always will, and I challenge every other Republican candidate to say the same thing or, if not, then to stop making silly assertions that their records and my records on immigration are the same."

Rubio gave tepid answers to his own immigration reform measures during the Dec. 15 primary. He refuted his role in amnesty talks two years ago, but said a Rubio presidency would allow immigrants to stay in the country legally if they paid a fine, passed a background check, received a work permit, and paid taxed. In the end, he warily conceded his immigration reform plan still includes a pathway to citizenship.

"That was the lesson we learned in 2013: there is no trust that the federal government will enforce the law, they (Americans) will not support you until they see it done first," said Rubio.

Republican lawmakers see Rubio and Cruz as viable, dependable nominees who can stretch outside their conservative voter base. More so than Trump can. Whether they can appeal to Latinos, the fastest-growing demographic in the country, may depend on whether Rubio and Cruz can still identify with their roots.

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