If Harris's early lead holds up, she will be the Republican nominee against Sen. Bill Nelson, D-Fla., in November, the Tallahassee (Fla.) Democrat reported.
At 9:15 p.m., with 38 percent of the precincts in, Harris had almost half the vote, the newspaper said. The remainder was split between three opponents, with her closest competitor, lawyer Will McBride, picking up about 30 percent.
Harris was the Florida secretary of state in 2000 and played a controversial role in the political and legal battles over whether Texas Gov. George Bush or Vice President Al Gore carried the state and the election. She was also hampered by a campaign contribution from Wade Mitchell, a defense contractor who has pleaded guilty to bribing Rep. Randy "Duke" Cunningham, R-Calif.
National and state Republican leaders tried to convince Harris to drop out of the race, but she refused.
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