Either is perfectly acceptable depending on what specifically you are trying to say. If you are referring only to presidents of the USA, then 'the' would probably be more precise, though 'a' would not actually be wrong in general terms.
However, there are presidents all over the place! I could be wrong, but I believe several wives of oriental presidents also ran for the office formerly held by their husbands. India, Sri Lanka and Indonesia all vaguely ring a bell along these lines, but perhaps you can google that to be sure.