By John Whitesides and Ellen Wulfhorst

MYRTLE BEACH, South Carolina (Reuters) - Democratic candidates Hillary Clinton and Barack Obama engaged in a bitter crossfire on Monday as their U.S. presidential campaign took an ugly personal turn on the Martin Luther King holiday.

Obama's complaints about former President Bill Clinton's attacks on him on behalf of his wife's campaign boiled over at a rancorous debate. Hillary Clinton flayed Obama for his praise of the late President Ronald Reagan, a Republican icon reviled by many Democrats.

The back-and-forth was so fierce that former North Carolina Sen. John Edwards, running a distant third in the Democratic race, accused them of squabbling and often had trouble getting a word in edgewise.

The Republican presidential contenders, meanwhile, flooded Florida ahead of a crucial showdown on January 29 in a nomination race where three different candidates have scored wins and a fourth, Rudy Giuliani, is looking for a breakthrough.

For Democrats, South Carolina is the next battleground in a seesawing race to find a candidate for the election in November. Obama, an Illinois senator, holds a slim lead in polls in the state, where more than half of the likely voters on Saturday will be black.

In the televised debate, Clinton accused Obama of praising ideas from the opposition party over the past 10-15 years after Obama said last week that Reagan "changed the trajectory of America."

"Now I personally think they had ideas. But they were bad ideas," said Clinton, a New York senator who would be America's first woman president. "They were bad ideas for America."

Obama, who would be the first black U.S. president, shot back that he was in no way praising Republican ideas, but simply saying that Reagan had been able to bring political rivals together.