Vice President-elect Joe Biden

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Jill says her husband's decision to accept the vice presidential nod came after a family discussion.

"Because I think Joe had the choice to be secretary of state or vice president. ... So I said, 'Joe, if you're secretary of state, you'll be away, we'll never see you, you know, I'll see you at a state dinner once in a while,'" Jill says. "But I said if you're vice president, the entire family—because they worked so hard for the election—can be involved. They can come to our home. They can go to events. They can be with us all the time. And that's what's important to us."

After the show, Vice President-elect Biden's spokeswoman Elizabeth Alexander denied Jill'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."