I know I'm not breaking any news to you here, but a parliamentary system would have plenty of negative consequences. The Framers didn't want a system that would be responsive to the passions and whims of the populace. They wanted a system that was stable and one in which change would be somewhat difficult. In fact, if factionalism was the greatest concern to the Framers then the two-party system has worked pretty damn well. It's hard to have extreme factions when everything is lumped into two categories.
If you ask me, the problem lies with the citizenry. The Framers expounded upon the need for citizens to be educated, moral, and frugal. Continence has given way to debt-fueled consumption. Age-old ideas about morality have given way to relativism. Education? It's now a means to an end, not an end in itself as the Framers believed. This is not to say that the Framers were correct philosophically, just that they designed a lumbering form of government with that type of citizen in mind.