As if his week needed to become any more challenging, Mitt Romney will appear in Miami on Wednesday to face some tough questions from a key group of voters crucial to his hopes of winning the White House – Florida's Hispanics.

The Republican presidential candidate, already in trouble for his "it would be helpful to be a Latino" comment recorded at a Florida fundraising dinner, goes into an interview with the Spanish-language TV station Univision seeking to explain and defend his controversial policies on immigration and healthcare.

Barack Obama, meanwhile, follows Romney to south Florida for his own appearance before the same cameras on Thursday. And while Obama enjoys a margin of popularity among Florida's 2.1 million Hispanic electors, 51% to 37%, according to the latest polls, analysts say the vote could yet tip either way.

"It's hard to win the presidency and not win in Florida, and it's hard to win in Florida without winning the Hispanic vote," said Casey Klofstad, associate professor of political science at the University of Miami and an analyst for the polling group Latino Decisions.

"The campaign is more about turnout than changing hearts and minds. The candidates need to court their base and go to where the votes are. The Latino vote is especially critical, and any candidate that comes through here needs to pay attention to it."

To treat the Hispanic community as a single entity, however, is a mistake neither candidate is willing to make as they pursue Florida's 29 electoral college votes. Aside from common concerns over jobs and the economy, each subgroup has its own issues and idiosyncrasies that the nominees will be attempting to address.

Both Romney and Obama are spending a disproportionate amount of time and resources here to get their positions across, and by Thursday night each will have visited Florida nine times since June 1, more than any other state during the campaign to date.

Republicans and Democrats are also lavishing more cash in Florida than anywhere else. According to Kantar Media, the Republicans spent $7.5m on advertising from July 1 to September 10, $1.5m more than the Democrats. Many of those TV commercials on both sides have been in Spanish, and have featured voters of Cuban or Puerto Rican origin or those of other Hispanic nationalities.

"This is a diverse and sophisticated electorate," Gabriela Domenzain, Obama's director of Hispanic press, told the Huffington Post.

"You can't just put out one message and think that speaks to 50 million people. We get that and we try to respect it."

Unsurprisingly, Romney is polling ahead of his rival among Cuban Americans in Miami, where exiles have traditionally supported successive Republican candidates for their hardline stance against the communist regime of Fidel Castro and his brother Raúl.

That is unlikely to change by November, but the demographic of Cuban Americans is undoubtedly shifting, as older, more conservative Cubans who fled the island in the 1950s and 60s die and the community increasingly consists of those born in the US.

Obama, therefore, has high hopes of a better showing among Cuban Americans, who make up a third of the Hispanic voting bloc and who were 63.9% in favour of Republican opponent John McCain in 2008.

"There has been a change in the thinking processes of many in the Cuban American community, and a realisation that what happens in Cuba is sometimes beyond the reach of what the American government can do," said Manrique Iriarte, a Cuban-born doctor who works at Miami's Mount Sinai medical centre.

"For five decades we've been hearing messages from both parties regarding the regime in Cuba. Politicians have been coming here for 50 years drinking coffee in Café Versailles and Cuba Libres on Calle Ocho – and it's not working any more. We're looking for broader messages for our lives as Americans.

"Most of the Cuban American vote will always be Republican no matter what happens or who runs for the White House, but the Democrats won 25% of the vote in 2000 and 35% in 2008. The goal is 40% this time, and that seems possible."

A different story for Puerto Ricans

Further north, Puerto Ricans are the fastest growing community in Florida and, to some observers at least, could have more of a say in deciding the eventual winner, largely because the group has no traditional party affiliation.

There are almost 900,000 Puerto Ricans in the state, double that of a decade ago, with migration promoted by a poor economy in their homeland and the fact that Puerto Rico's status as an unincorporated territory of the US grants them citizenship and freedom of movement.

Puerto Ricans now account for 28.4% of Florida's Hispanic electorate, according to Pew Research Center figures, and are on course to become the largest group by the 2016 election. About 350,000 live along the so-called I-4 corridor from Tampa to Daytona Beach, where voters could determine the contest one way or the other if the rest of the state stays loyal to the Republicans in the north and the Democrats in the south.

It also explains why a raft of senior Democrats including the Obamas and Bill Clinton, and several politicians from Puerto Rico, have been regular visitors. The president even stopped by a Puerto Rican café in Orlando last month for a photo op with a plate of pulled pork, rice and beans.

"For us, like others, the economy and healthcare are the big issues, and I would say the majority are Democrats," said Maria Luyanda, head of her own Orlando-based insurance company and president of the Puerto Rican chamber of commerce of central Florida.

"The main reason is which party tends to protect the middle class and which party protects rich people. Many of us are small business owners and we look to who will look after us."

Romney's stated policies on immigration, experts say, remain an obstacle to his building support among other Hispanic voters, notably the smaller yet significant communities from Mexico (8.9%) and the Dominican Republic (4.5%). Romney has said he would veto the proposed Dream Act, which offers a path to citizenship for children of undocumented immigrants, and that he supports self-deportation and stiff penalties to those who entered the US illegally or outstayed visas.

Obama, by contrast, announced in June he was suspending the deportation of hundreds of thousands of undocumented immigrants between 16 and 30 and would instead give them work permits, something Romney now says he supports.

"It would be better for Romney to peel away from immigration and pivot to the economy," said Klofstad, the professor at the University of Miami where Romney's Univision interview is taking place.

"He needs to say that most important is job creation and the economy, it's something we can all agree on, and here's what I'm going to do."

Then there's Romney's claim in a secretly filmed video at a dinner for donors in Boca Raton, Florida, that if his Mexican-born father had native parents instead of American expatriates: "I'd have a better shot of winning this."

The comment infuriated many, and it remains to be seen how much of Florida's Hispanic vote it will cost him in November.

For now "there's no doubt the Romney campaign has been hit hard," Klofstad said.