How long could our country possibly last if..?

Forever, in theory. It's an interesting point you make though, and a very progressive one. The only thing a country needs in order to survive is sovereignty and citizens. Though our political system makes a mockery of rational thought, some things aren't messed with by us, or the system really. In particular, neither party is going to end the military and if 80% of us died off for some reason, it's likely that half if not all the rest would be drafted. So "check" to both requirements. The fact that you think whether or not our democracy is going to solve more specific and less critical matters like health care or education has anything to do with our continued existence, shows that you have evolved to believe that true existence requires happiness and fulfillment. Take whatever comfort you can from knowing that on the most basic of principles, neither side disagrees.