This is a political expression, which refers to voting blocks upon which the politician can rely. In the case of Mr. Obama, it refers to voters who will reliably vote for the Democratic ticket, and who will, especially, reliably vote for him. If those voters become convinced he can't win, then they might not vote. No one would expect his base to vote for a Republican, but if they are downcast, they might not vote at all. So an American politician seeks to attract uncommitted voters--so-called independents--who, when added to his or her base, will get enough votes for a victory. But a politician cannot ignore his or her base, his or her reliable supporters, because he or she will still need those voters to go to the polls on election day and vote.