IN the last hour of the last day of registration, as shadows lengthened across Lauderdale Manors, canvassers from the Florida Immigrant Coalition hustled from door to door in search of eligible voters.

Their T-shirts read: "I Vote! Do You? Yo Voto! Y Tu? Eu Voto! E Você?" – the same urgent question in English, Spanish and Portuguese.

By law, they did not advocate support for either party, but in this desperately poor African-American neighbourhood, there was no doubting who would benefit from increased participation. The only person to mention either presidential candidate by name was an eight-year-old boy, who said, "We got to vote for Obama because we need our food stamps", as if to back up Mitt Romney's infamous description of a society in which 47% of the people are dependent on government.

Henrique Lelis, finding a family that had recently moved house, talked them through the registration process. The young parents showed their driving licences, provided social security numbers and signed up.

"We meet people who thank us for coming to their door to register them, but also people who are scared: they have the right to vote, but doubt our motives," Lelis said. "Some people don't believe who we are and don't want to show their papers. I tell them, 'You are passing the responsibility of voting to somebody else who maybe isn't such a good person.'"

The sun dipped behind rows of mustard-yellow bungalows and a fight broke out. As the two men brawled with bare fists, three others filmed the action on mobile phones. It was a show born of boredom, but the anger in their eyes was real and the best blows landed with a sickening crack. There were only a few minutes before the registration forms had to be delivered and the violence was a good reason to leave.

Florida is the largest swing state, with 29 electoral college votes. Bill Clinton is the only president in the modern era to win the White House without carrying Florida; no Republican has done so since Calvin Coolidge in 1924. Romney must win here.

The state can be roughly divided in three: the northern counties have much in common with their conservative neighbours, Georgia and Alabama; Miami's sprawl is a Democratic stronghold, and the central area either side of the I-4 motorway is evenly split – and one of the most fiercely contested regions in the US.

George W Bush's official margin of victory over Al Gore here was 537 votes out of almost six million: still a bitterly controversial result 12 years on. Polls show this year's contest is a dead heat, raising the prospect of another legal battle over voting irregularities.

In the last three decades, the number of eligible Latino voters in the US has tripled, but most of this growth is in states such as California and Texas where there is no question which party will win. However, in Florida, the votes of Spanish-speaking immigrants could be decisive.

Unlike most Latino communities in the US, which have roots in Central and South America, two-thirds of Florida's Hispanic voters come from Puerto Rico or Cuba. As the former are born US citizens and the latter can claim political asylum, immigration policy is much less important to them than to families from Mexico. Interestingly, Cuban-Americans tend to vote Republican, although this is changing among a younger generation with no memory of Communism.

In a recent poll of registered Latino voters, the economy and immigration were tied as the most important election issue, at 30% each, but as Norma, a Florida Immigration Coalition canvasser, told me, it can be difficult to separate the two. "Immigration is still the number one concern, because it has an impact on employment, health care, education," she said. "All of these things are more difficult to get if you're undocumented."

Back at the office, the volunteers counted their forms. They had added 118 voters on the last afternoon of a three-week drive. Their co-ordinator, Sean, urged them to hurry to make the 7pm filing deadline.

The Brazilian Community Centre in Pompano Beach is, for now, a patch of bare, cracked concrete the size of two football pitches. Jonathan Rodrigues, a US citizen born to Brazilian parents, told me that political consciousness has developed gradually, over generations. "Every year that passes, there will be more citizens, more involvement in politics," he said. "When children are born to immigrants, they have to deal with healthcare, with education. This is when political involvement begins."

Four years ago, Barack Obama won 67% of the Latino vote, and their continued support is crucial to the Democratic party. In June, the president granted two-year deferrals from deportation for young immigrants who were brought to the US as children, have been here for five years, have no criminal record and have completed high school or served in the military. The Pew Hispanic Centre estimates 1.4 million people could be eligible.

Larissa Salvador arrived aged 11 with her parents and has spent half her life in the US. At school, she was top of her class, but when she finished, her options were limited as she was not a legal immigrant.

She said: "It was incredibly painful. I had no idea what to do and was angry with my parents for bringing me here. Without documents, you worry that people are going to ask to see your visa, you can't drive, you aren't anybody. I was made here, but I'm always being told that I don't belong."

Now she has won a scholarship to study criminal justice in New York. When her deportation deferral comes through, she plans to apply for a job in the district attorney's office. "I understand why Obama took so long to do anything," she said. "When he did, it was like a prayer being answered. This was a chance to be a normal person. I started crying and didn't stop."

But many Latinos are disappointed with the failure to pass more comprehensive immigration reform – and there has been a record number of deportations during Obama's tenure: 1.1 million people.

This was an opening for Republicans, but in a primary campaign characterised by nativist rhetoric and support for Arizona's harsh new immigration law, it seemed as if the Grand Old Party was doing its best to drive Hispanic support away. The short-term political calculation is that it may be more important to fire up the white base than reach out to Latinos: in the 2010 congressional elections, fewer than a third of registered Hispanics voted.

The apathy of this reliably Democratic group was one reason for that party's crushing mid-term defeat. Another was that white senior citizens – a Republican bedrock group – turned out in droves. In Florida, where pensioners cast one in five ballots in 2008, elderly voters are the most powerful constituency of all. In Coral Ridge, a wealthy neighbourhood of retirement homes two blocks from Fort Lauderdale beach, Romney-Ryan signs outnumbered Obama-Biden by ten to one.

Down by the pier, Bernie and Denise Radochonski were enjoying the morning sunshine. "It's impossible for anyone to say that they're in better condition than they were when the president was elected," Bernie said. This is almost true: according to the latest census figures, incomes for the richest Americans rose by 4.3% last year, while everyone else's fell.

The perception of economic stagnation is dangerous to the president, though unemployment continues to fall. Fisherman Michael Ferraro said: "I'm leaning towards Romney. I haven't seen much of a change." Four years ago, he voted Obama.

The one issue that could torpedo Romney in Florida is Medicare – specifically his running-mate Paul Ryan's plan to transform it into a voucher scheme. Two-thirds of the state's senior citizens say they want the programme – the closest thing the US has to our National Health Service – to continue unchanged. Asked who they trust to secure it, elderly voters consistently favour Obama, by up to 20%.

Romney's campaign accuses Obama of "raiding $716 billion from Medicare" to pay for the Affordable Care Act. Over pictures of white, worry-lined faces, adverts warn that "the money you paid for your guaranteed healthcare is going to a massive new government program that is not for you".

Carol Berman, 77, spends her free time tackling these misinformation claims head-on in Golden Lakes, the West Palm Beach retirement community where she lives. She has been campaigning for healthcare reform since her first husband developed Alzheimer's and she had to divorce him to avoid being bankrupted by care bills. She has had a tumour removed, four operations on her back and lacks a large intestine since contracting ulcerative colitis. She takes 16 different pills every day, but only gave up her job in a Ralph Lauren shop six months ago.

"I tell people you have to vote as if your life depends on it, because it does," she told me. "To my chagrin, I find that a lot of people who really need this programme don't seem to get it. My neighbour is on long-term disability and has a daughter with Down Syndrome, so they are both collecting from the federal government. Someone like that is in danger of losing those benefits, yet he points his finger at me and says, 'You've been brainwashed.'

"Some of these people who don't seem to understand what you're telling them, you find they're genuinely racist and just do not want a black president."

This is one reason the Republican party's nightmare vision of an entitlement society – where the taxes of hard-working Americans rise to support an ever-growing pool of leeches – remains so effective.

At the pier, Sicilian-American pensioner Barney Zarzana, another New Yorker flown south, told me: "It was nice that we had the first black president, but he didn't do anything, he's just a professor."

He voted for George Bush twice and though he didn't see the point with John McCain, he will vote for Romney: "He's a smart man, a businessman, and in this country, that's what we need."

In Pompano Beach, Jonathan Rodrigues pointed out: "If the Republican Party continues to win the same percentage of votes among the same demographic groups, by 2020 it will lose by 14%." But this year, in this election, it just might be enough to take back the White House.