* Florida is a big prize in presidential race
* Most recent polls tipped Romney to win key battleground
* Conservative U.S. Representative Allen West trailing
Americans gave President Barack Obama a second term in office, but it still wasn't clear early on Wednesday whether the president won the key battleground state of Florida.
The vote in the state, which introduced the terms "hanging chads" and "butterfly ballots" to the masses in its historic 2000 presidential election, was too close to call long after Republican challenger Mitt Romney conceded his loss.
Early Wednesday morning Obama was edging out Romney by about 45,000 votes, or 0.53 percentage points, out of a total of 8.27 million votes cast in Florida, with about 99 percent of the votes counted.
"It's 1:42 in the morning and I just heard there are still people voting in Miami-Dade County," tweeted Chris Cate, spokesman for Florida's Secretary of State, who is responsible for elections. "Kudos to their commitment to voting!"
The head of elections for Florida's Miami-Dade County, which accounts for about 10 percent of the state's 12 million registered voters, said final results would not be available until Wednesday afternoon.
Until then, it may not be totally clear whether Obama won the state, which he carried in 2008.
At one church in Miami hundreds of voters were still in line when polls were due to close at 7 p.m.
"I believe that Obama is doing a good job and he's going to do a better job," said Michele Adriaanse, 59, who arrived to vote at 6.30 p.m. and finally cast her ballot shortly before midnight. "If we don't give him the chance, things will go back to how they were," she added.
Miami-Dade Supervisor of Elections Penelope Townsley told reporters the delay was due to "an extremely high volume of absentee ballots" and because long lines forced some precincts to remain open hours after their official closing time.
Florida accounts for 29 of the 270 votes in the electoral college a candidate needs to win the presidency. That is more than any other swing state, and by many accounts the fourth-largest state was a must-win for Romney.
Most recent polls had given Romney an edge over the incumbent in Florida, where the economic recovery has been slower than in other states and long-term unemployment has reached record highs.
But registered Democrats outnumber registered Republicans in Florida by about 5 percentage points and Romney faced multiple headwinds in the state.
A plan by Romney's vice presidential running mate, U.S. Representative Paul Ryan, to change the Medicare health insurance program for seniors was among the factors often cited as holding back Romney's campaign in the retiree-heavy state.
He also suffered from an inability to make inroads among Hispanic voters, outside of the state's conservative Cuban-American community.
Florida propelled former President George W. Bush to a wafer-thin victory in 2000 when he won the state by 537 votes.
Complaints about voting procedures, long lines to cast ballots, restrictions on early voting and some possible irregularities have been heard repeatedly across Florida. There have been no claims of anything widespread or problematic enough to cast doubt on the credibility of the Florida outcome.
It also was not immediately whether U.S. Representative Allen West - the firebrand Republican lawmaker known for his blistering attacks on Obama and other Democrats - had won one of the country's most closely watched congressional races.
West, a darling of the conservative Tea Party movement, had amassed one of the largest campaign war chests among House Republicans. His known supporters included organizations like Americans for Prosperity, the conservative political advocacy group funded by the billionaire Koch brothers.
But he faced a tough re-election challenge against Democrat Patrick Murphy, who had hammered the first-term Republican for the intransigence that led to gridlock in Washington.
Early Wednesday morning, West, 51, was trailing by 2,000 votes out of the 318,000 ballots cast.
Murphy, a 29-year-old businessman and political newcomer, had strong backing from party headquarters and was one of the best-funded Democratic challengers in the country.
A certified public accountant whose father runs a construction company in Miami, Murphy turned the race into a referendum on West, calling the Republican an extremist member of a "do-nothing" Congress.
The battle in Florida's new 18th district was seen as a test of whether a high-profile - some say polarizing - conservative could win one of the biggest swing districts in a perennial swing state.