Details from sciencemag.org (A magazine from the American academy for the advancement of science):
https://www.sciencemag.org/news/2020/02/united-states-badly-...
https://www.sciencemag.org/news/2020/02/united-states-badly-...
Wow this is frankly insane. Pretty much every biology laboratory in the USA should have the tools available to perform these tests. More than that, RT-PCR is a routine assay that any self-respecting wetlab biologist can do. If they are struggling to produce these kits they should be letting people order their own primers. Even if less reliable, at least then they would be able to test patients properly.
Edit: I suppose you do need a "self respecting wetlab biologist" to synthesize the primers, but running the test itself is pretty simple.