WASHINGTON – Joe Biden's wife said Monday that he had his pick of being Barack Obama's running mate or the secretary of state nomination that eventually went to Hillary Rodham Clinton, a slip that the vice president-elect immediately tried to shush.

Jill Biden's comment came during an appearance with her husband on "The Oprah Winfrey Show," taped at Washington's Kennedy Center on the eve of the inauguration.

"Joe had the choice to be secretary of state or vice president," she said. Her husband turned to his wife with his finger to his lips and a "Shhhh!" that sent the audience into laughter. "OK, he did," Jill Biden said in her defense...

After the exchange aired on television three hours later, Biden spokeswoman Elizabeth Alexander denied Jill Biden's account in a statement e-mailed to reporters.

"To be clear, President-elect Obama offered Vice President-elect Biden one job only — to be his running mate," the statement said. "And the vice president-elect was thrilled to accept the offer."

While the statement denies that Obama ever offered Biden the secretary of state job, it doesn't rule out that the two discussed the possibility. Obama's transition office did not respond to questions about their private discussions.