While the first option would be unwise, the second would also be unwise.
A complete shutdown for a disease as virulent as Covid-19 will just suppress the virus for the duration of the shutdown. Ignoring the extreme difficulty and impracticality of shutting society down for a moment, recognize that the moment the shutdown ends, the virus will probably reappear and continue to spread.
What then? Another complete shutdown? When does it end?
No, the right solution is a distributed solution in which affected companies and communities deal with the virus, imposing gradual restrictions on gatherings, work, schooling etc in an organic way. Which is exactly what is happening in the US right now.
The point of all this is, what more can the US government do than it is already doing? Send the military in to shut down the highways? Hold scientists at gunpoint until they produce a vaccine?
Many (Media, Democrats) are trying to leverage this to their political advantage, but aside from small changes in approach, what exactly do they want the government to do differently?