COLUMBIA, South Carolina (Reuters) - South Carolina Democrats voted on Saturday in a bitter presidential nominating race, with Barack Obama leading Hillary Clinton in polls and counting on heavy black support to carry him to a needed victory.

Voter turnout was heavy soon after polls opened at 7 a.m. under cloudy skies and chilly temperatures around much of the state, with long lines at polling places reported in early morning balloting.

Record turnout of more than 300,000 is expected in the first Democratic primary in the South, where black voters are likely to make up about half of the electorate. Polls close at 7 p.m., with results available soon afterward.

“I am absolutely convinced that we can win here, and we can win anywhere in the country,” Obama, an Illinois senator, said at a late-night rally in Columbia that capped a week spent campaigning heavily across the state.

South Carolina is the latest test for Obama and Clinton, a New York senator, in their escalating battle for the right to represent the Democratic Party in November’s presidential election.

After two consecutive losses, in New Hampshire and Nevada, Obama needs a win on Saturday if he hopes to head into the February 5 “Super Tuesday” contests in 22 states with a realistic chance of victory.

The high stakes fueled a week of angry accusations, harsh advertisements and increasingly personal jabs between the two candidates, capped by a volley of attacks on Obama from Clinton’s husband, former President Bill Clinton.

Hillary Clinton spent Saturday chatting with voters in two restaurants before heading to Tennessee for a town hall meeting in Nashville, leaving South Carolina before polls close.

The other candidate in the Democratic race, former North Carolina Sen. John Edwards, chastised his two rivals for their squabbling and ran ads promoting himself as the grown-up in the contentious nominating battle.

Edwards said the tone of the South Carolina contest was disappointing: “There’s been a lot of effort by the other two candidates to tear each other down which is why I’m focused on the voters and doing positive things.”

OBAMA LEADS

A Reuters/C-SPAN/Zogby poll on Saturday showed Obama with a 41 percent to 26 percent edge over Clinton in South Carolina, with Edwards in third place with 19 percent.

The lead for Obama, who would be the first black U.S president, is fueled by his 62 percent support among black voters, the poll found. Clinton and Edwards are tied among white voters at 35 percent, with Obama at 19 percent.

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Clinton left South Carolina for two days during the week and headed to states with contests on February 5, leaving her husband to carry the campaign load here.

All three candidates have portrayed themselves as the strongest leaders of a shaky economy. Clinton has hammered Obama for a lack of experience and highlighted her readiness to lead “from day one” in the White House.

But Obama questioned her judgment on Friday, noting her vote in 2002 to authorize the Iraq war and her failed stewardship of the health care overhaul during Bill Clinton’s administration.

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“It’s not a question of being ready on day one,” he said at an evening rally in Florence, South Carolina. “It’s a question of being right on day one.”

The Republican presidential contenders, who held their primary in South Carolina last week, are focused on Florida’s Tuesday primary.

Arizona Sen. John McCain and former Massachusetts Gov. Mitt Romney are in a tight race in Florida, polls show, after splitting contests last week -- McCain won South Carolina and Romney won Michigan.

In St. Petersburg on Saturday, Romney peddled his economic message to factory workers, telling voters America needs an outsider to shake up Washington.

“I know something about it. I know a lot about it,” he said of the economy. “I don’t think someone from the inside is going to able to turn Washington inside out.”

McCain took aim at Romney’s experience, telling a rally in Fort Myers: “I believe it is important not to have been a manager but a leader...I can hire a lots of managers, but I believe I am qualified to lead and I have the record to prove it.”

Former New York Mayor Rudy Giuliani is desperately seeking a good showing that could get him back in the race. Giuliani, who once led the Republican field in national polls, has slipped after he essentially pulled out of the early voting states to concentrate on Florida.

(Additional reporting by Ellen Wulfhorst, Tim Gaynor, Deborah Charles, Jason Szep; Editing by Vicki Allen)