I feel the real question is “can the black American who calls himself a Christian vote for Obama?” And the obvious answer is no. Obama and the Democratic party stand for so many anti-Christian things it would take a book to list them all. It is a travesty that black Christians allow themselves to still be owned by the Democratic party.
Without trying to be too judgmental, I would say there is decent chance, they either don't know the Lord, or they don't know the issues.
If the DNC wants blacks to vote for a black Christian, they should have nominated a black Christian instead of nominating a tan Arab Muslim.