The Constitution originally left it up to the States as to who could vote and who could not, although later Amendments would spell out (and expand to) a near universal adult enjoyment of the voting franchise; making adult suffrage the Constitutional (but not entirely originalist) position.
A democracy cannot exist as a permanent form of government. It can only exist until the voters discover that they can vote themselves largesse from the public treasury. From that moment on, the majority always votes for the candidates promising the most benefits from the public treasury with the result that a democracy always collapses over loose fiscal policy, always followed by a dictatorship. The average age of the world’s greatest civilizations has been 200 years.
~~ http://www.lorencollins.net/tytler.html