The following correction was printed in the Guardian's Corrections and clarifications column, Tuesday October 14 2008

We were wrong to say in the article below that about 10 million registered Jewish voters live in Florida. Florida currently has about 10.7 million registered voters in total, of whom about 5% are Jewish. This has been corrected.

This year Kenny Furst came close to breaking the habit of a lifetime. Brought up in a Jewish neighbourhood in the Bronx, New York, under Roosevelt's New Deal, he is and always has been a Democrat. But this year, for the first time, the 90-year-old was veering towards voting Republican or not at all.

The problem was Barack Obama. "He's the first Democratic candidate I haven't been sure about. As far as I was concerned he was connected with the Arabs," Furst said, speaking in Tamarac, Florida, where he retired to 18 years ago.

For his wife Selma, 87, as for many Jewish Americans, the ties to the Democratic party were also umbilical. Yet she did not like the idea of an African American president, and was worried about rumours that Obama was a secret Muslim. Then something happened.

Their grandson announced he was flying from Los Angeles, 2,500 miles away, to visit. Mike Bender had learned of an internet-driven initiative to get young Jewish voters to make a "great schlep" to Florida to persuade their wavering grandparents to vote for Obama.

The viral movement was backed by a video message by the comedian Sarah Silverman, saying: "You know why your grandparents don't like Obama, because his name sounds scary. Yes Barack Hussein Obama is a super shitty name, but you'd think somebody named Manishevitz Guberman would understand that."

Bender watched the video, laughed, and decided to traverse the States to confront his grandparents.

He was not alone. Over the weekend dozens of young Jewish Americans travelled to Florida with the ambition of swinging this ultimate swing state in favour of Obama. Hundreds more have made the lesser schlep, or "mini schlep" - lobbying their grandparents by phone.

The thinking behind it starts with the assumption, widely held by political analysts, that if John McCain, is to have any chance he must win Florida. Democrats have taken the state only three times in the past 12 presidential elections: Lyndon Johnson in 1964; Jimmy Carter in 1976; and Bill Clinton in 1996. But the contest has frequently been close, famously so in 2000 when George Bush squeezed into the White House with just 537 more votes in Florida than Al Gore.

That sense of opportunity explains why the Obama campaign has posted hundreds of staff in the state and is spending a record $39m (£23m) there, far more than McCain. The investment has to some extent paid off, with polls showing a three-point lead, though that falls within the margin of error.

Which is where the Jewish vote comes in. About half a million registered Jewish voters live in Florida, mainly older people in retirement condominiums along the so-called Gold Coast. Most are lifelong Democrats originating from New York and the north-east, but this year there is estimated 13% who, like the Fursts, are undecided. That equates to up to 100,000 votes: enough to determine the outcome of Florida, and with it the fate of the nation.

"The number one way to influence the outcome of the election as Jewish people is to influence your grandparents in Florida," said Ari Wallach, an instigator of the great schlep.

Those who embarked on that schlep found the going was sometimes tough. University student Cobin Dopkeen, who flew from Boston, had no need to convert his grandparents who are already for Obama, so instead accosted other residents and visitors in their retirement complex in Miami. Which is when he met Lenny, a 62-year-old Floridian out for a walk with his 92-year-old father.

"You have to be out of your fucking mind to support Obama," was Lenny's reply. "Number one: he supports Hamas. Number two: he sat with Reverend Wright for 20 years as he spieled out his antisemitic hatred."

And Lenny doesn't want a black president. "I grew up in the sixties when blacks were called nigger. OK, nowadays I say N-word, but I still think it."

Republicans in south Florida predict a 10% spike for McCain in the Jewish vote over the 24% polled by Bush in 2004. Their campaign line is that if Obama wins he will be the first pro-Palestinian US president since the foundation of the state of Israel. The Democrats hit back with leaflets showing Obama by Jerusalem's Wailing Wall wearing a yarmulka.

From most schleppers' experiences, the unbending hostility of Lenny was the exception. Many reported a warm reception from most Jewish Americans in Florida who are already in the Obama camp. Others notched up success stories, including Bender's grandparents.

His visit moved and impressed. It led to long conversations in which he sought to allay their fears. Obama was a Christian, he said, a vocal supporter of Israel who has pledged to work for all Americans. The final hurdle was convincing his grandmother that Obama was not a Muslim. "I said to her that if there are any people who can understand the wickedness of lies said about them, it is the Jews. That hit home."

Within a day of their grandson's arrival, the Fursts had declared for Obama and had begun proselytising with the zeal of the newly converted. Kenny Furst has been posting Obama flyers at the bagel shop where he still works, and his wife is holding discussion groups with other Jewish women from the retirement home.

"I'm so proud of my grandparents, that they were open-minded enough to listen," said Bender.

"I've got a couple of years to go, so this vote isn't for me," said his grandfather. "All I'm interested in now is that my grandchildren should be safe. This one is for them."