One couple said they would not leave until they are issued a marriage license, said Diana Bradrick, chief deputy recorder clerk.
About 55 protesters staged a "sit-in" throughout the day in the county clerk's marriage room, singing and chanting, but otherwise acting "very polite," Bradrick said.
The protesters will be allowed to stay unless they interfere with the office's business operations or if they refuse to leave at closing time at 5 p.m., Bradrick said.
If they won't leave voluntarily, the Sheriff's Department, which handles building security, will ask them to leave, she said.
Three same-sex couples who requested marriage licenses from the county clerk today were denied, Bradrick said.
"They are being told that by state law, we are not able to issue a license to a same-sex couple," she said.
Tuesday's decision by the California Supreme Court upheld the passage of Proposition 8, which amended the state constitution making marriage only between a man and a woman.