Sortition is a process by which public officials are chosen through a lottery of citizens, not an election. I.e., one day, you get a call to become President of the United States.
I don't know whether or not they considered sortition explicitly, but in general they were skeptical of the ancient Greeks (who used sortition). They instead preferred the Roman tradition, which emphasized elections.
They were creating a republic, not a democracy. They saw the Greek democratic tradition as a dangerous form of mob rule. A republic is really a type of oligarchy, just with the oligarchs chosen through election. This was especially the view of the Federalists; the Republicans led by Jefferson were what passed for populists back then, and were less oligarchic--at least in theory.