Ginty was put up as a candidate by conservatives who don't like the younger Kean's support for abortion rights and embryonic stem-cell research. Some observers have said that if Ginty garners a big chunk of the vote it could dampen Kean's prospects.
Kean has been viewed the GOP's best Senate hope in years in a state that has not elected a Republican to that body since 1972.
Menendez was appointed in January by Gov. Jon Corzine to serve out the remaining year of Corzine's Senate term. He handily defeated his primary opponent, James D. Kelly Jr., who lives in a group home for the mentally ill.