This is an important point, from a former head of the CDC:

A surge in people being tested could actually spread disease, because people can become infected by someone else waiting to be tested. Getting tested today is no guarantee you won’t get infected tomorrow — and may give you a false sense of security. Furthermore, emerging data suggests that testing of throat swabs may miss as many as two-thirds of infections.

From my point of view as an infectious disease control physician, it’s dismaying to see both the promises of and demands for widespread testing that, if met, will do little good and possibly some harm.

He goes on to note the circumstances where testing is important, but general testing for those with no current or only mild possible symptoms is not.  He makes other good points in the articles as well, and you can follow him on Twitter here.  I hope someone with power is listening to him!