The party issued a statement Thursday saying they had won Florida. The Associated Press has not declared a winner because the contest is too close to call.
Obama led Romney 49.9 percent to 49.3 percent, or by about 52,000 votes. Obama won the White House even though Florida is still undecided.
The Romney campaign and the Republican National Committee said they are waiting for the state to finish its count, which includes thousands of provisional ballots.
Florida is still undecided largely due to long voting lines on election night, a deluge of last-minute absentee ballots and other assorted problems.
Rod Smith, chairman of the Florida Democrats, attacked Florida Gov. Rick Scott - a Republican - for refusing to extend early voting hours, saying it was "a serious mistake that should and must be corrected."
The race results were so close that they could trigger a recount, bringing back memories of the 2000 election, though this time, the votes would hardly matter.
Under Florida law, the state's secretary of state could order a recount if Obama's lead over Republican challenger Mitt Romney finished below a half-percentage point. A manual recount could be ordered if that recount ended below a quarter-percentage point. On Thursday, Obama led Romney 49.9 percent to 49.3 percent - about 9,000 votes over the recount threshold.
Romney's campaign could waive the recount.
Secretary of state spokesman Chris Cate said it was unclear how much a recount would cost taxpayers.
Miami-Dade County suffered the bulk of glitches and long lines, with some voters waiting until 1:30 a.m. Wednesday to cast their ballot. The county's supervisor of elections, Penelope Townsley, said she was aware of the criticism of how her office handled the election.
"I think Miami-Dade County conducted a very good election," she said Thursday. "Am I embarrassed or disappointed by some of the things that happened? Absolutely. But, I have to focus on simply getting it right. And that is exactly what I will move to do."
Officials vowed to figure out why lines were so long; some speculated it was the length of the ballot (there were 12 statewide constitutional amendments) while others blamed the reduction of early voting days from 14 to eight by the Republican-controlled Florida Legislature.
The long lines prompted frustrated residents like Jorge Lopez-Bernal to call the state "a joke."
Miami-Dade Mayor Carlos Gimenez asserted: "this is not a third-world country."
"The waits were way too far," Gimenez said. "And we've got to get some answers as to what happened. Why? Why wasn't it foreseen?"
Gimenez said he would ask Gov. Rick Scott to extend early voting hours in future elections.
Scott didn't return calls on Thursday about the voting problems from the AP. On Wednesday, he said he was willing to look at whether changes are needed to make voting go smoother.
Scott came under a barrage of criticism after he refused to use his emergency powers to extend the number of days of early voting.
Scott said he will sit down with state election officials soon to discuss ways to improve the election.
Another cause of the vote logjam was absentee ballots and the fact that voters had until 7 p.m. Tuesday to drop them off.
Officials in several counties said voters handed in the sealed envelopes containing the ballots shortly before polls closed Tuesday evening, and elections workers needed to verify the signatures and run the ballots through the voting machines. In Pinellas County, there were about 9,000 such ballots and it took most of the day Wednesday to process them.
Lush reported from St. Petersburg. Suzette Laboy also contributed from Miami