* Three of Florida's 67 counties still tallying votes
* Governor denies blame for gridlock
* Large Hispanic turnout heavily favored Obama
By Tom Brown
MIAMI, Nov 8 (Reuters) - Florida's Democratic Party declared victory for President Barack Obama in the closely divided battleground state on Thursday, as he clung to a narrow but apparently insurmountable lead in the glacially slow tallying of votes from Tuesday's election.
If Obama wins Florida, it will add to his Electoral College margin and he will have won all of the key U.S. swing states except North Carolina, which he carried in 2008.
"On behalf of Florida Democrats, I wish President Barack Obama congratulations on his re-election and on his winning Florida's 29 electoral votes," Rod Smith, chairman of the Florida Democratic Party, said in a statement.
In a tacit concession, Republican Party of Florida spokesman Brian Burgess said in an email that he and other Romney supporters were "obviously not happy with the result" in the Sunshine State.
"But given the wave that we saw all over the country, we're glad that we gave them enough of a fight in Florida to prolong the battle here as long as we did," Burgess said.
As of Thursday evening, Obama had 49.92 percent of the statewide vote, versus 49.22 percent for Romney, according to the Florida Division of Elections.
Two of the three counties where ballots were still being tallied, Broward and Palm Beach, are heavily Democratic. The third county, Duval, has more registered Democrats than Republicans but has traditionally leaned Republican in presidential contests.
Just 58,055 votes separated the two candidates, but that was far more than in the 2000 election, when Republican George W. Bush won Florida by 537 votes and captured the White House after a recount dispute that reached the U.S. Supreme Court.
The slow-moving vote count in Florida has already made it the brunt of jokes on late-night television and conjured up ugly memories of the situation 12 years ago, when Florida was the cause of electoral gridlock.
This time, Florida seemed almost seemed irrelevant since Obama handily won re-election without its 29 electoral votes - the biggest prize of any of the nine key U.S. swing states.
HISPANICS FOR OBAMA
No officials were willing on Thursday to predict exactly when the race in the fourth most populous U.S. state, which has 67 counties, would be officially declared as decided. But barring any big surprises, Obama looked set to get a bump from Florida that would lift his electoral vote count to 332 over 206 for Romney.
"It's appalling that two days after the election, Florida was not able to report our presidential election results," Smith said in his statement.
"This embarrassment lays at the feet of Governor Rick Scott, who made a decision to cut early-voting in half and continually refused to extend early voting hours in light of the record turnout," Smith said.
In comments earlier in Orlando, the Republican governor adamantly refused to accept responsibility for Florida's failure to hold an election that was free of controversy.
Scott's decision not to extend early voting, after it was cut back to eight days from 14 by the Republican-controlled legislature, has been cited by many Floridians as a cause of exceedingly long voter lines on Tuesday.
Scott told Reuters, "We did the right thing" when asked about the decision, which many saw as a move to blunt voter turnout for Obama.
The length of ballots, which included 11 proposed state constitutional amendments backed by the legislature, has also been blamed for long lines at polling places and delays in tallying final results. Scott said: "The amendments don't go through the governor. The amendments only go through the legislature."
Smith attributed Obama's victory, at least in part, to what he described as "the strongest, largest ground game" Democrats had ever mounted in Florida, all part of a carefully calculated get-out-the vote effort.
The Obama campaign also cited a large turnout by the state's 1.4 million Hispanics, who voted heavily for the president. Obama won a record 61 percent of Hispanic votes in Florida, up from 57 percent in 2008, according to exit polling data compiled by Bendixen & Amandi, research and media consultants for the Obama Hispanic campaign.
Democrats made surprising inroads in the Cuban-American community, capturing 48 percent of the traditionally conservative Cuban-American vote, according to Bendixen & Amandi, surpassing the 35 percent mark set by Democratic President Bill Clinton in 1996.
"This really is a sea change," said Sergio Bendixen, a longtime Miami pollster. "The Cuban community is no different from anywhere else in the country. It is lower middle-class, it does not have health insurance and it wants to have it. It counts on Medicare and Social Security and it's finally figured out which party is defending their interests."
He said the growing population of 380,000 Puerto Ricans in central Florida was also pivotal. They preferred Obama over Romney by a margin of 83 percent to 17 percent.