Despite President Obama's advantage with the Latino voters, boosted after his immigration announcement Friday, Republicans are not ceding the Latino electorate, focusing instead on how the country's sluggish economy and high unemployment rate has been especially hard on Latino voters.

Just days after Obama announced his administration would not seek to deport up to 800,000 children of illegal immigrants, the Republican National Committee came out with a new web video in both English and Spanish, and a research piece that hit the president for the nation's economic problems and how they had disproportionately hurt Latinos.

Over the voices of news coverage telling the viewer "Latino unemployment is in the double digits" are images of both the president and struggling families.

"After four years of President Obama, our economy isn't better," a graphic reads before these statistics appear over a woman looking through her bills: "Hispanic unemployment skyrocketed to 11 percent" and "2.3 million more Hispanics in poverty."

The video says more Latinos are likely to be uninsured, before it ends with a clear message: "While Obama plays politics, Hispanics are suffering in the Obama economy."

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In a nod to the hand-to-hand combat for every vote in this race, the RNC and the Romney campaign will continue to go after Latino voters despite the president's polling advantage.

A Bloomberg poll released Tuesday surveyed likely voters after the president's move, and 64 percent agreed with Obama's policy, while 30 percent disagree. The survey did leave voters divided along party lines, with 86 percent of Democrats favoring the measure while 56 percent of Republicans opposed it. Other polls have shown a nearly double-digit jump in support for Obama among Hispanics since he made the change, and the president was already doing well among the country's largest minority. An ABC News/Washington Post poll earlier this spring revealed 73 percent of Latinos backed Obama, compared with 26 percent for Romney.

The new policy is similar to the Dream Act, supported by Obama, but rejected by Republicans in Congress. It will offer temporary work permits to young illegal immigrants who were brought to this country by their parents.

Latinos have cited the economy, not immigration reform, as their top priority in the election. One statistic that could favor Romney and shows an opening with this part of the electorate.

Mitt Romney has voiced opposition to the new White House policy saying he favors a "long term measure," but declining to say whether he would reject the executive order if he wins the election in November.

Like the web video, he has accused the president of playing politics with the move, saying in one Fox News interview it was "partly political" and in another that he was trying to "shore up his base with Latino voters."

"I believe that the reason this came out is the president's trying to shore up his base with Latino voters, and he's also trying to change the subject from his miserable speech last week, from his gaffe that the private economy is doing fine, and from the failure of his economic policies to get this economy going again," said Romney Tuesday in an interview with Fox News radio.

Also Tuesday, there was a conservative uproar when ABC News' Jonathan Karl reported Marco Rubio was not being vetted to be Romney's running mate. As the party's top Hispanic conservative, sources told Karl it was "dumb politics" not to consider the young charismatic Florida senator. Romney came out Tuesday evening and said he was indeed being vetted, which may even help with some Latinos.

Both the president and the presumptive GOP nominee will continue their outreach to the Latino community this week. They both address the annual National Association of Latino Elected and Appointed Officials conference in Orlando, with Romney speaking on Thursday and President Obama on Friday.