Even still, we just can't scale up PCR like that.
If it costs tens of billion dollars, so be it. That's far cheaper than shutting the economy for months at time.
This is essentially a war-time effort we are in. I believe government has the authority to mandate that companies with relevant manufacturing capability build and sell these machines in order to combat the virus.
However, sufficient availability of supplies and equipment for this scale of operation is a pretty big if.