I see no problem in giving federal money for these testing and contact follow through. However I see in my mind that millions of dollars will be wasted. One state suggested that every student should be tested before being let in the schools and then every student tested once a week until a vaccine and cure can be provided.
I say give the share of the monies to each state based on population of the state on the last census. They will then be able to pick companies or hospitals to run this testing program based on a plan of how to test the population at random. Contact test would then be done based on the initial test.
The Governors might want to think about using their own National guard to do the collection and forward to a testing facility in the state