MIAMI, Fla. – With the nation’s largest battleground state in a dead heat, the subtlest shifts in allegiances among Florida’s Hispanic voters could decide the state’s 27 electoral votes.

Just like in 2000, President Bush continues to lead among Hispanics here, and particularly among Cuban-Americans. But Democrats say the growth of the non-Cuban Hispanic population and an aggressive get-out-the vote drive have blunted the president’s advantage enough to net thousands of additional votes for Mr. Kerry in a state that Mr. Bush won by just 537 votes four years ago.

Republicans scoff at the theory, predicting that Mr. Bush will do better among Hispanics around the country than four years ago.

Both sides have poured unprecedented sums into Spanish-language advertising and have been flooding the state with surrogates and activists trying to get out the vote. Rep. Nydia Velazquez, a Democrat of New York, is one of many out-of-towners parachuting into the Sunshine State today for the final push at the request of the Kerry campaign.

In 2000, President Bush won 210,000 more Hispanic votes than Albert Gore. Even a modest change in Mr. Kerry’s favor could reverse the outcome, Democrats say.

“If one half of 1% of the Cuban-American community had stayed home, it would have been more than enough to let Gore win,” said a former executive director of the Cuban American National Foundation, Joe Garcia, who is advising the New Democrat Network, a group courting Hispanics for the Democrats.

Democrats believe the growth in the non-Cuban Hispanic population works in their favor.

“We think there is going to be a huge growth for Democrats in Florida. We’re not only talking about the Cuban-American community, but Salvadorans, Columbians, Venezuelans, Puerto Ricans. Many for them are voting for the first time, and a year ago were not aligned with any party,” said a spokesman for the pro-Democratic group, Guillermo Meneses.

They were heartened by a recent Miami Herald/Zogby International poll of likely voters in the heavily Latino Miami-Dade County, the most populous county in the state. It found that Mr. Bush’s lead among all Hispanics had shrunk compared to 2000, even though it remained unchanged among Cuban-Americans. Mr. Bush was leading Mr. Kerry by 62% to 35% among Hispanics in the county a week before Election Day. In 2000, Mr. Bush had a 73% to 27% victory over Mr. Gore.

Mr. Garcia predicted Mr. Kerry will gain five to seven percentage points among Cuban-Americans, who voted more than 80% of whom voted for Mr. Bush in 2000. But he also predicted that Mr. Kerry will gain 14 points among non-Cuban Hispanics, 60% of whom voted for Mr. Gore and 39% for Mr. Bush in 2000.

Democrats also see what they call a “historic” opening into the traditionally stalwart Republican Cuban-American community, gambling that recent arrivals and second-generation voters are more concerned about health care than they are about Fidel Castro.

Mr. Kerry is hoping that many Cuban-Americans are upset about the Bush policy of restricting travel and money flowing to Cuba, which makes it difficult for recent arrivals to help their families back home. At a recent rally in Miami, he condemned the policy and criticized the president for ignoring Latin Americans.

The demographics show a changing Cuban-American profile, said a pollster with the firm Mason-Dixon Polling and Research, Inc., Larry Harris.

“It’s not a monolithic Cuban vote any longer. We need to make a distinction between Cuban versus second and third generation Cuban, who are not waking up wondering if this is the day Castro is going to go. They are voting more like your average American,” Mr. Harris.

The New Democrats group estimates that older Cuban exiles, who are overwhelmingly supportive of Mr. Bush, represent 67% of the Cuban-American electorate, or 250,000 voters.

A poll conducted for them in July showed that among the 75,000 who arrived after the 1980 Mariel boatlift, 40% favored Mr. Kerry to Mr. Bush’s 29%, with the rest undecided. The poll also suggested that almost 60% of the 50,000 Cubans born in America backed Mr. Kerry.

But Republicans say the Democrats are misguided. A Florida state legislator, David Rivera, was one of 13 Cuban-American members of the Florida House of Representatives who sent a letter to the president a year ago asking him to take a “more dramatic” stand against Mr. Castro to galvanize the community.

“Among the hard-core Cuban-American voters in the exile community, there has been overwhelmingly support,” Mr. Rivera said. “Maybe be among recent arrivals, there may be less enthusiasm, but recent arrivals aren’t eligible to vote because they are not citizens.”

He predicted that the president “will match or exceed his performance among Hispanics” today.

A Bush campaign spokeswoman, Sharon Castillo, said that any Democrat who thinks Cuban-Americans will overlook the issue of Fidel Castro “just doesn’t get it.”

“Cuban-Americans are not going to vote for someone who has a history of making Castro’s life easier,” she said.

Republican strategists expect Mr. Bush will capture 40% to 42% of the Hispanic vote nationwide, up from 35% in 2000. That will require doing even better in Florida than four years ago, said Ms. Castillo, who did not have specific predictions for Florida.

“We know that the Latino community overwhelmingly supports this president. This is a president who knows the Latino community and we know him. We are family to him, he speaks our language, and he has delivered policies that have bettered the lives of Latinos across the country,” Ms. Castillo said.

Another recent poll of national Hispanic voters suggests the Bush campaign will have to work hard to reach that target. A Miami Herald/Zogby poll conducted October 26-29 showed 61% of Hispanic voters backing Mr. Kerry, and 33% backing Mr. Bush. The Bush campaign is spending $5 million on Spanish advertising nationwide this year, up from $2 million in 2000. It has paid for 28 Spanish language ads, all of which have run in Florida, Ms. Castillo said.

The New Democrat Network has poured $2.5 million into advertising the Democratic message on Spanish language television and radio in Florida since last March, compared to less than $1 million spent nation-wide by the Gore campaign in 2000.

In 2000, there was also record turnout among Cuban-Americans in the wake of the seizure of Cuban drifter Elian Gonzalez.

But political observers are predicting a record turnout on all sides due to the close and emotional election and numerous get-out-the-vote efforts.

Hispanic Republicans are also expected to come out to vote for Republican Senate candidate, Mel Martinez, a Cuban-American who is running against Democrat Betty Castor, a former president of the University of South Florida and a former education commissioner.