I HATE that idea! Way to European. What's the point in even having a revolution if you're just going to hand the reigns of power back to an inbred elite? (Give it a few generations and such a system will produce family trees that make the Hapsburgs and Rothschilds look simple) I perfer the idea of titles of nobility going to elected officals (Lord Senator, Lord Representive etc) and being non-herditary, and the King being elected from amoung them. In America anyone can grow up to be King.
The founders were already quite anti-populist (or elitist, depending on how you look at things) as evidenced by the electoral college, senatorial elections through state legislatures, vetoes and the powerful Supreme Court. It was all designed precisely so that not anybody can grow up to be President, or at least not any populist.
If they're going for a monarchy, what makes you think they'll be moving to a more democratic system at the same time? I see two options: symbolic (hereditary/elected) or powerful (probably not hereditary). Probably have the monarch be crowned by both houses of congress, with the voters either getting to confirm a set of options presented by congress, or being cut out of the monarch selection system and voting for representatives and their state legislatures instead.
If it were hereditary, no idea who they'd seriously consider. A European would definitely be a symbolic/ceremonial monarch filling out the role of Head of State. Maybe they'd let it be hereditary with an American monarch, but with significant fetters on their powers and a recall mechanism for when/if the dynasty becomes unpopular/dies out/succession crisis.