We are currently quarantining about 300 million here in the US, so tens of thousands would be a massive improvement.

The way to think about this is: who do we need to test so we can start un-quarantining people.

The goal is not to find out who has it because right now, we are essentially behaving as if the entire US population is infected. The goal is to efficiently determine who is very unlikely to have it so that those people can start incrementally returning to normal life.

It's not worth testing symptomatic people: they've already "failed" one test in that we at least know they have symptoms. Simply continue to treat them as infected.