“Yes, but most presidents don’t appoint political opponents to their cabinets, especially to prominent/ powerful positions like Sec of State. Generally speaking, the vice-president is not a politically powerful position, though it can be a springboard for a future presidential run. In recent years, a presidential candidate’s selection of a running mate has become opportunity to broaden one’s demographic/ political appeal (see John McCain & Sarah Palin). Thus choosing one’s former political rival as a running mate is a practical move that can help a candidate achieve a win that otherwise wouldn’t have been possible. There is no similar political advantage to appointing a competitor to a Cabinet position.”
anon, cabinet positions can (and are) often used as bargaining chips in behind the scenes political deals. Clinton was damaging Obama’s chances of becoming president, and she would never quit just to help him out.