Paul Clement, who served as U.S. solicitor general under President George W. Bush and is now a lawyer in private practice, is the favorite of many conservatives. Clement argued last month for the Supreme Court to strike down Obama's 2010 healthcare law, and he is defending laws that ban same-sex marriage and that target illegal immigrants. Clement, 45, would be "at the top of any short list right now," said Curt Levey, executive director of the Committee for Justice, a group that advocates for conservative nominees. Asked about Clement, Mary Ann Glendon, a co-chairwoman of Romney's Justice Advisory Committee, voiced...