Sorry to say this, but the US is going to be even worse than Italy. You have not been testing nearly enough people.
A large public system cannot be conjured out of thin air to met each crisis.
We will see the large well funded social medical systems, with their “inefficient” over capacity, over-perform the operating on thin margins private systems.
I’m terrified here in the US.
(FWIW - give me 90% socialized medicine with room on the margins for private clinics, like the vast majority of the 1st world)