Yes. Roche just got FDA approval on a SARS-COV-2 test that will take four (4) hours that works with two of their (whatever you call the machine) models. Per Roche there are around 110 of those machines in the United States. Bloomberg had estimated throughput numbers and also indicated that Roche has tests that work with some of their other, slower equipment (that I assume is in the US as well).
Mayo Clinic recently developed a 2 hour test.
The limits on testing are, from my POV, entirely political at this point.
https://www.npr.org/2020/03/13/815522836/u-s-coronavirus-tes...
https://www.bloomberg.com/news/articles/2020-03-13/roche-get...