According to ESPN's Tony Kornheiser, who was at the Capital Hilton for the dinner, O'Connor said that of the two leading Republican candidates, "one is a practicing polygamist, and he's not even the Mormon."
Romney is a Mormon, and often points out that he and his wife, Ann, have been married for 42 years. Gingrich's three marriages have been much discussed in the campaign. The Reliable Source column in The Washington Post had a similar account.
Chief Justice John Roberts and Justice Anthony Kennedy also are Alfalfa Club members. O'Connor was among the first group of women admitted as members in the 1990s.
Associated Press writer Matthew Lee contributed to this report.
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