Sen. Marco Rubio of Florida has been mentioned as a possible vice presidential candidate on the GOP ticket.

Story highlights

Sen. Marco Rubio of Florida often mentioned as possible GOP vice presidential candidate

The son of Cuban immigrants, he strongly opposes illegal immigration

New Mexico's Susana Martinez is also seen as a possible VP

Miami CNN  — 

Will he or won’t he? And would it matter?

Florida Republican Sen. Marco Rubio, considered a powerful Hispanic political player and rising star in his party, has consistently said no to having vice presidential aspirations. But still, the question keeps coming up.

Rubio, the popular Miami-born son of Cuban immigrants, has been seen by some inside Republican circles as a great “get” as a possible No. 2 on a hypothetical presidential ticket, and is already showing his power to influence the process.

Just this week he pushed back on former House Speaker Newt Gingrich after the Republican presidential candidate ran a Spanish language radio ad labeling former Gov. Mitt Romney as “the most anti-immigration candidate.” Rubio called the commercial “inaccurate” and “inflammatory” and the Gingrich campaign pulled the ad.

Gingrich press secretary R.C. Hammond said the ad was taken down as part of a scheduled “rotation time for the ads,” not as a result of complaints from Rubio.

Team Gingrich takes down Spanish-language ad

“This kind of language is more than just unfortunate. It’s inaccurate, inflammatory and doesn’t belong in this campaign,” Rubio told the Miami Herald.

So, did his defense of the former Massachusetts governor constitute an endorsement? No. Rubio spokesman Alex Conant told CNN, “We remain neutral.” Neutral, but perhaps not detached.

Romney and Gingrich are in a statistical dead heat in Florida, according to the latest CNN/Time/ORC International Poll.

What would Rubio bring to a Republican ticket? Many believe he could pull the Hispanic vote and clinch the victory in November. But others remind us there is no one single Hispanic vote but rather a complex group united only by a common language, with heritages as diverse as Cuba, Mexico, Puerto Rico, El Salvador or the Dominican Republic. In 2008, Hispanics voted 67% for then-Sen. Barack Obama over Sen. John McCain, who received 31% of their votes.

Navarrette: GOP, don’t blow it with Florida’s Latinos

Juan Hernandez, a Republican strategist and CNN en Español political contributor, offers caution. “Marco Rubio is well-liked among Hispanics but he must speak clearly in favor of immigration reform to bring votes to a Republican candidate for president.”

Immigration is an area where Rubio differs from other Hispanic elected officials. He recently said that immigration isn’t the sole issue for Hispanic Americans. But as a wedge issue, it makes many Latinos – even those registered as Republicans – feel uncomfortable when the candidates talk about border security while rejecting the legalization of some undocumented workers and demanding that America makes English its official language.

There are those who believe that Rubio, a Cuban-American, would have a hard time attracting Mexican-Americans, who represent seven out of every 10 Latinos in the United States.

At the CNN debate in Jacksonville, Florida, on Thursday night, the candidates were asked about which Hispanics they would include in their administration. Rubio was first on the list for a Cabinet slot from Rick Santorum, while Gingrich suggested the senator might be more suited for a more “central and dignified” role than a Cabinet post.

Hernandez, a Mexican-American, said he believes there are other people besides the Florida senator worth looking at. “Rubio has notoriety today, but there is much room for leadership in the Hispanic political arena,” he said.

Romney talks about possible running mates

Another name that comes up as a potential vice president is Susana Martinez, the Republican governor of New Mexico whose name was also mentioned Thursday night. Martinez is a Mexican-American conservative, but like Rubio, her position on immigration is in sharp contrast to where many Hispanics are on the subject.

She wants to revoke driver’s licenses from undocumented immigrants in her state and signed an executive order requiring state police to check the immigration status of “criminal suspects.”

But Maria Cardona, a democratic strategist and CNN political contributor, doubts Martinez can deliver the Latino vote. “Gov. Martinez would be a better match to garner any Latino support than Rubio ever would,” she said. “But even so, she did not win the majority of the Latino vote in her state and if the VP nominee, presumably she would mirror the GOP nominee on all issues, which would mean she would be on the wrong side of most issues important to Latinos and so it would still be an uphill for her to garner enough Latino support for the GOP ticket.”

“Latinos vote on the issues, not on surnames.”

CNN’s Jim Acosta contributed to this report.