A top aide to Sen. Hillary Rodham Clinton who is a member of one of Buffalo's best known political families has been quietly building a candidacy for lieutenant governor in 2006, according to several sources. Leecia R. Eve, Clinton's counsel and daughter of former Deputy Assembly Speaker Arthur O. Eve, has contacted Democratic leaders in Buffalo and around the state about running for the No. 2 post. Erie County Democratic Chairman Leonard R. Lenihan is one who has discussed the race with Eve. "She's definitely exploring the possibility of running for lieutenant governor, and she certainly comes with the credentials," Lenihan said. Few others have publicly discussed running for lieutenant governor, a post that often adds ethnic and geographical "balance" to the ticket. Attorney General Eliot L. Spitzer, who is Jewish and from Manhattan, is the top Democratic contender for governor next year. That leads to speculation that an upstate, African-American woman could broaden his appeal in the general election.