The Constitution contains the term "natural born" for a US president. This term was used to prevent anyone with the possibility of having a foreign allegiance from becoming commander-in-chief of US forces, for obvious reasons (super fifth column, anyone?) A person with dual citizenship owes allegiance to both the US and the foreign government. They are required to obey the laws of both countries, which of course for a sitting US President would be disastrous to the US nation.
The term "natural born" is used to mean a singular allegiance to one and only one nation. Dual citizenship contradicts this.
(Note that it is unique that the US president is also the commander-in-chief, which entrusts the office of president with great power, so a concern of allegiance was on the minds of the framers of the Constitution. Senators and Representatives can be naturalized; the President cannot, because of the Commander-In-Chief power.)
All NATURALIZED citizens have to take an oath of ALLEGIANCE, to confirm they only have allegiance to the US and no other country. But this is not enough to fully repudiate possible allegiances to other countries.
So "allegiance" is the key here -- at the time of the writing of the US Constitution, "natural born" was a term carefully chosen to define that allegiance - it means having a singular allegiance that derives from one's having been born of the soil of the nation - in this case, the US nation. This results in a kind of "super-allegiance".
That is what the framers meant, and Constitutional lawyers have always recognized this to be the meaning.
So according to the Constitution, which explicitly and unambiguously uses with the term "natural born" when referring to qualifications for someone to be the US president, no, a US president cannot have dual citizenship. They must have that singular allegiance that can only be derived from having been born of US soil - "born here".
