With the GOP presidential nomination no longer in doubt, President Obama and Mitt Romney this week are urgently turning their focus to Hispanic voters — a group whose alienation from Republicans threatens GOP prospects for winning the White House and has given the Obama campaign an early opportunity to lock in the support of a key constituency.

Sensing a chance to exploit the disconnect, the Obama reelection campaign is accelerating its efforts to reignite the intensity that brought out Latino voters in record numbers four years ago.

The Republican nominee-to-be and his party are looking to repair relations by dispatching organizers to critical states and by reminding Hispanics that the administration has not lived up to its promises on immigration reform.

At a private fundraiser Sunday night in Palm Beach, Fla., Romney told supporters that “we have to get Hispanic voters to vote for our party” and warned that a big win of that group by Obama “spells doom for us.”

His comments were overheard and reported by journalists for NBC News and the Wall Street Journal.

For the Obama team, the new push begins Wednesday, when the campaign announces its first round of Spanish-language television and radio ads. The initial spots — to be aired in Colorado, Nevada and Florida — will feature Latino Obama volunteers promoting the president’s education policies.

In one, Daniella Urbina, a Harvard University graduate raised by her mother and grandmother, says: “Financial aid is very important to the Latino community. I was the first in the family that was going to go to college. I think President Obama understands us.”

In coming weeks, Obama’s campaign will intensify its Latino phone-banking operation and send canvassers door to door to find even relatively small pockets of Hispanic voters in states such as New Hampshire.

Its Web site features a Spanish-language calculator on which voters can compare their tax rate with Romney’s. And the president has become a regular presence on Spanish-language media, having done 15 interviews since his inauguration on the Univision Network alone.

The stakes for both sides are heightened by the math and the map. Hispanics are the nation’s largest and fastest-growing ethnic minority, accounting for more than 16 percent of the population. They also make up crucial voting blocs in two-thirds of the swing states where the presidential election is likely to be decided.

The urgency is being felt most intensely in the battleground states.

“The key to this thing is what percentage of Hispanic votes we get in Florida or Virginia or Ohio or Colorado or Nevada or New Mexico,” said Al Cardenas, the former Florida GOP chairman who is advising the Romney campaign on how to reach out to Hispanics. “He needs to get close to 40 percent in six states.”

On Monday, the Republican National Committee announced that it has appointed state directors to drum up Hispanic support in Florida, Nevada, Colorado, New Mexico, Virginia and North Carolina.

“In order to win their hearts and minds and votes, we’re going to have to share our own vision for a better tomorrow,” Cardenas said, “and we’re going to have to do it in a way where the community feels they are part of us.”

For the former Massachusetts governor, reaching anywhere close to 40 percent of the Latino vote will be a tall order. A survey released Wednesday by the Pew Research Center showed Obama beating Romney 67 to 27 percent among Hispanics if the election were held today.

Washington Post polling since the beginning of the year suggests both difficulty and opportunity for Romney. Only 32 percent of Hispanics have a favorable view of him in polls over the past month, compared with 39 percent who have a negative one. On the other hand, 30 percent have yet to form an opinion. By comparsion, Obama is viewed favorably by 67 percent and unfavorably by 29 percent.

Sen. Marco Rubio (R-Fla.), a rising star who has been talked about as a potential running mate for Romney said: “When you hear these anti-illegal immigration voices . . . they sound as if they are not just anti-illegal immigration. They sound like anti-immigration and anti-immigrant voices. The vast majority of Republicans don’t talk that way, but, unfortunately, all the voices that talk that way happen to be Republicans.”

But there are signs that Latinos are not as enamored with Obama as they once were. A Gallup poll this month, for example, found that his job approval among Hispanics was only nine percentage points above the national average; in earlier surveys, it had run as much as 20 points above the overall number.

Although Obama is not likely to lose the Latino vote to Romney, he may have trouble motivating enough Latinos to come to the polls, said Matt Barreto, a University of Washington political science professor who heads the nonpartisan polling firm Latino Decisions. “More people are less excited this year.”

Still, Romney’s problems run deeper.

During the primaries, Romney ran to the right of his GOP rivals on immigration, criticizing Texas Gov. Rick Perry for signing a law that would grant in-state college tuition rates to illegal immigrants and clashing with former House speaker Newt Gingrich over whether there should be what Gingrich called “some level of humanity” in allowing long-term illegal residents to stay in the country. Romney called Arizona’s controversial immigration enforcement law — which is set for argument next week before the Supreme Court — “a model” for the nation.

“I cannot see any possible path right now for Romney to get anywhere near 40 percent [of the Hispanic vote] outside Florida,” where there is a strong contingent of conservative Cubans, Barreto said. “They have done so much damage. . . . It will be very difficult for them to backpedal that.”

Romney insisted, however, that it is possible. “We’re going to be able to get Hispanic voters,” he said at the fundraiser Sunday. “We’re going to overcome the issue of immigration.”

One potential inroad that Republicans are looking to is a scaled-back version of the Dream Act being crafted by Rubio. The original bill, which enjoys overwhelming support among Hispanics, would offer a path toward citizenship to children who were brought to the country illegally by their parents. Rubio’s proposal would allow them to study and work in this country legally on a non-immigrant visa.

But Rubio said his bill — which he said is “designed to address a very small and select group of people, young people, who find themselves undocumented through no fault of their own” — would not do much to address the deeper divide that has grown between between Latinos and the Republican Party.

“The broader issue that I’ve outlined is not the kind of thing you can just put together and do in a PowerPoint presentation,” he said. “It involves a real commitment to both the rhetoric and the policy that, over time, will allow you to make a compelling argument that, at a minimum, they should give us a chance, election by election.”

Polling analyst Scott Clement contributed to this report.