Joel P. Bennett, the lawyer for one of the women who has made accusations against Mr. Cain, said that his client had decided not to go public or to make a public statement herself in an effort to shield herself from the media frenzy swirling around the situation. “She’s not going to affirmatively make any public statements or public appearances about the case, everything will be through me,” Mr. Bennett said. “She has a life to live and a career, and she doesn’t want to become another Anita Hill.”