Obama, as President of the United States, is also the Executive head of the State Department.  Please review the following current policy of the Obama administration as to dual nationality:

The U.S. Government recognizes that dual nationality exists but does not encourage it as a matter of policy because of the problems it may cause. Claims of other countries on dual national U.S. citizens may conflict with U.S. law, and dual nationality may limit U.S. Government efforts to assist citizens abroad. The country where a dual national is located generally has a stronger claim to that person’s allegiance. However, dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there. (Emphasis added.)

The Obama administration policy is that dual nationals owe allegiance to the foreign country as well as the US.  The law applies the President.  If he is a dual national, he owes allegiance to “foreign powers“.

See this link for detailed explanation of the effect of certain international Acts, their dates, and their effect on Obama’s dual citizenship, which Barack Obama HIMSELF acknowledged on his campaign website!