Are you sure they did? At the time republicanism was in vogue because Roman classicalism was currently in fashion. However these same men (particularly Hamilton) spoke very negatively about democracy, considering it a road to tyranny.
So at the time, democracy was considered absurd and perhaps evil. But were republics? The UK had an experience with republicanism before America, under Cromwell (that left a bad taste in the mouths of many monarchists) but even so it changed the way a lot of people thought. John Locke for instance predates the American revolution.