Updated: 4:57 p.m. Vice President-elect Joseph Biden had the choice of being either secretary of State or vice president in the Obama administration, but ultimately decided on the No. 2 job for family and other reasons, Biden’s wife, Jill, said Monday afternoon. The Bidens were taping an episode of the “Oprah Winfrey Show” from the Kennedy Center in Washington, D.C., and discussed with the talk-show hostess how Biden had made the decision to join the Obama ticket as his running mate. “Joe had the choice to be secretary of State or vice president,” Jill Biden said, drawing a gasp from the audience. She said the two discussed the option, and decided that the job of vice president would allow for more family time. Jill Biden said she worried that if her husband headed the State Department, he would travel so frequently she would only see him “at a state dinner every once in a while.” Joseph Biden acknowledged that it was “corny,” but said he based the decision on how he could best serve the country and the Obama administration. Shortly after the taping concluded, a spokeswoman for the vice president-elect sought to downplay the remarks, saying that Obama only offered Joseph Biden one job: the vice presidency. “Like anyone who followed the presidential campaign this summer, Dr. Jill Biden knew there was a chance that President-elect Obama might ask her husband to serve in some capacity and that, given his background, the positions of Vice President and Secretary of State were possibilities,” Elizabeth Alexander said in a statement. “Dr. Biden’s point to Oprah today was that being Vice President would be a better fit for their family because they would get to see him more and get to participate in serving more. To be clear, President-elect Obama offered Vice President-elect Biden one job only – to be his running mate. And the Vice President-elect was thrilled to accept the offer.” Airing of the news that Biden was given the chance to take the spot that Obama later offered to his former presidential primary rival, Sen. Hillary Rodham Clinton (D-N.Y.), could be seen as a slight to the former first lady. Sen. John Kerry (Mass.), the 2004 Democratic presidential nominee, also had expressed interest in the secretary of State job.