04/19/2012 06:02 pm ET Updated Apr 19, 2012

Mitt Romney May Not Get Boost Among Hispanic Voters With Latino Vice President Pick

Picking a Latino running mate would not help Mitt Romney much with Hispanic voters, according to a poll released on Thursday.

That could throw a kink in what some Republican strategists believe is a possible game plan for winning more Latino voters, who so far aren't flocking to the candidate.

The poll, released by Project New America and Democratic outfit Public Policy Polling, asked Hispanic voters in Florida, Nevada and New Mexico about their preference between President Barack Obama and Romney. Florida, Nevada and New Mexico, respectively, are home to Sen. Marco Rubio, Gov. Brian Sandoval and Gov. Susana Martinez, who all have been named as potential Republican picks for vice president.

In all three states, a majority of the Latino voters polled chose Obama over Romney, which aligns with other polls on Hispanic voter preferences.

More interesting, though, are the results on whether voters preferred a ticket with Obama and Vice President Joe Biden or a ticket with Romney and a prominent Latino politician from their state.

When asked about if Rubio were to be added to the ticket -- rather than about just the presidential candidate alone, Latino voters in Florida did not opt for Romney to a greater degree. Forty-four percent of these voters said they would vote for Romney in both situations.

In Nevada, 26 percent of Latino voters said they would choose Romney over Obama. That percentage climbed to 27 percent when voters were asked about adding Sandoval.

There was a similar result in New Mexico, where 27 percent of Latino voters said they would support Romney in a match-up with Obama, and 28 percent said they would support Romney and Martinez over Obama and Biden.

Of course, voters' preferences about at least two of those candidates might not matter: Rubio and Martinez have each said they would decline if asked to be on the ticket.