The current nucleic acid tests don't require hours of work. Each individual testing reaction requires probably less than 1 minute of a technician's time to set up (e.g. probably a total of 30 minutes bench time to set up a single 96-well run). The 2-3 hours' time is what it takes for the reactions to proceed (i.e. waiting time that the technician can use to set up the next batch of tests). The backlog is due to lack of sufficient facilities and trained personnel to do these tests, or in many cases, unwillingness to repurpose what we already have to do this.
With a single set up of basic research-lab type equipment that was available in the late-1990s, costing less than $5000 in total, a single technician could easily run 400 tests in a single workday. With pooling, that would allow testing 2000 people per day. Give the same technician access to 5 such setups, and/or modern automated equipment, and she could process close to 10,000 tests in a single day.
So basically, for the annual salary of one superfluous administrator, and a week or two to train a few unemployed bartenders, any university or school district could set up its own testing system sufficient to test all of its students almost every day, using the most sensitive techniques available. Hell, most large universities already have all this equipment and grad students who know how to use it times 50. We don't need a federal "Manhattan Project" to do this.
Neither does waving a magic wand or looking into a crystal ball. The "instant tests" that are currently available, and the technology that exists today that could be used to create better ones, are not very sensitive or accurate.
