Humanity got by without a lot of things for a very long time. But around 1800, the population begun to climb. After taking 200,000 years to reach our first billion we, reached our seventh just 200 years later. A sudden reversion to the conditions known by America's Founding Fathers would leave ~7/8th of the global population unsupported.

So yes, flush toilets would be the least of your concerns, what with the zombie apocalypse in full swing and everything.