While Senator Hillary Rodham Clinton and her advisers insist that she is determined to win the Democratic nomination, friends of the couple say that former President Bill Clinton, for one, has begun privately contemplating a different outcome for her: As Senator Barack Obama’s running mate. The reports about Mr. Clinton’s musings surface as the Obama camp has quietly begun the process of searching for a partner on the Democratic ticket. The prospect of an Obama-Clinton ticket has been fodder for political gossip for months, with some Democratic leaders pushing the idea as a way to unify the party. The Obama...