Earlier this month, Obama announced that his administration would stop deporting illegal immigrants who come to the country at a young age and meet certain requirements. The directive is particularly popular among Hispanics, with more than 90 percent saying they’re in favor of the policy change.

The president's directive has placed Republicans on the defensive, with Romney's campaign caught between Hispanic outreach efforts and large segments of the GOP base, which regards the new policy as amnesty.

After Obama’s announcement, Romney offered support for easing deportations but said he believed the decision could make it more difficult to achieve comprehensive immigration reform.

Romney is against the DREAM Act immigration reform proposal, which is overwhelmingly popular among Hispanics — 87 percent support it, according to the poll — and has praised Arizona’s controversial immigration law, the majority of which was struck down by the Supreme Court this week.

Latino Decisions/America’s Voice poll, also released on Wednesday, shows the challenges facing Romney as he works to build Hispanic support. Forty-two percent of Hispanics surveyed in that poll said Republicans were not concerned about the issues that are important to them, while 31 said the GOP was hostile to issues favored by Hispanics. The poll also found that a majority of Hispanics — 55 percent — know someone who is an undocumented immigrant.

While Obama could be nearing his ceiling of Hispanic support, the NBC/WSJ/Telemundo poll found Hispanics are not as enthusiastic about his candidacy as they were in 2008.

Sixty-six percent of Hispanics said they were very enthusiastic, down from 68 last month. The same poll from July of 2008 found 80 percent of Hispanics to be extremely enthusiastic about Obama, and that number grew to 92 by November of that year.

Obama won the Hispanic vote 67 to 31 over Sen. John McCainJohn Sidney McCainCNN's Ana Navarro to host Biden roundtable on making 'Trump a one-term president' Mark Kelly clinches Democratic Senate nod in Arizona Prominent conservatives question Jerry Falwell Jr. vacation photo MORE (R-Ari.) in the 2008 election.

Obama will need to maximize turnout among this key constituency in what is lining up to be a tight election, especially in swing-states like Florida, Virginia, Nevada and Colorado that have large Hispanic populations.

The NBC News/Wall Street Journal/Telemundo poll was conducted from June 20 to 24 and has a 5.7 percent margin of error. The Latino Decisions poll was conducted between June 12 to 21 and has a 2 percent margin of error.