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Romer’s on leave from NYU at present, says Wikipedia. On ABC Australia this week, he was saying 9 billion tests per year, $100 billion - otherwise lockdown to some degree:

3 May: New Yorker: Paul Romer’s Case for Nationwide Coronavirus Testing
By Isaac Chotiner
Paul Romer, a Nobel Prize-winning economist who has served as the chief economist at the World Bank, has been putting forward plans to mitigate the economic fallout from the coronavirus and to allow for a return of normal economic activity in the U.S. His main proposal is to offer bimonthly tests to every person in the country, allowing more of us to go about our daily lives safely...
I recently spoke by phone with Romer, who is a professor at N.Y.U. During our conversation, which has been edited for length and clarity, we also discussed why Americans may be resistant to digital contact tracing, the need for states to administer tests, and what lessons economists have learned from the crisis...

ROMER: “Listen, you need the perspective of economics to say that, right now, this depression is costing us, in an order of magnitude, back-of-the-envelope, five hundred billion dollars per month. So, if we can come up with a solution that costs us like eight to ten billion a month, we’re way ahead. And so don’t worry about whether we can afford to do the testing compared to the alternative. We can obviously afford it.”...

“If you had said to me in 2019, “Pandemics are a really big threat. We should be spending a hundred billion a year to test people frequently,” I would have said, “Oh, I’m not really sure if you’d have to go that far.” I would have been skeptical, too. It seems like maybe overkill. It’s a lot.”...
“But now we should look at the feasible alternatives, one of which is that we let this virus just spread through the entire population. That’s going to kill at least a million people. And what people haven’t grappled with yet is that that process of it spreading through the population is itself going to take a year. So, this is not a quick path to reopening the economy, even if you’re willing to sacrifice that many people. On the other hand, if what we’re doing is using social distancing and staying away from each other, whether it’s compelled officially or just automatic because we’re afraid, if that’s the way we’re keeping the replication number of this virus below one, we could be in this depressed state for eighteen months, twenty-four months, a long time. And I think it’s going to become politically unsustainable.”
“So then, if you revisit a million people dead or a depression for eighteen to twenty-four months, a hundred billion on tests seems, to me, like a walk in the park.”...

NEW YORKER: I guess drinking bleach could work.

ROMER: “No, no. Let the record show I did not respond to that remark.”...
https://www.newyorker.com/news/q-and-a/paul-romer-on-how-to-survive-the-chaos-of-the-coronavirus

8 May: FactCheck (Annenberg Public Policy Center): How Many COVID-19 Tests Are ‘Needed’ to Reopen?
By Jessica McDonald
“Testing is still limited,” Michael Mina, an epidemiologist at the Harvard T.H. Chan School of Public Health, told us in response to Pence’s statement...

The question of how many tests it will take is hotly debated, with some groups recommending at least around half a million tests a day, and others suggesting several million or upwards of 20 million or even 35 million a day...

When asked whether “any worker who’s nervous about going back” would have access to both diagnostic tests for the virus and antibody, or serological tests, “right now,” Trump replied, “There should be no problem.”

But Yonatan Grad, a professor of immunology and infectious diseases at Harvard, said the answer “is quite clearly no,” adding, “we don’t yet have the capacity to offer broadly either virologic or serologic testing.”

National Institute of Allergy and Infectious Diseases Director Anthony Fauci told CNN’s Jake Tapper on April 28 that everyone who needs a test, “according to the way we’re approaching the identification, isolation, contact tracing, keeping the country safe and healthy,” should be able to get one by the end of May or the beginning of June.
“That’s what I’m being told by the people who are responsible for the testing,” he added. “I take them for their word.”...

On the other extreme, there’s Nobel laureate and New York University economist Paul Romer’s plan to test the entire U.S. population once every two weeks, or around 25 million tests a day. He has since raised that to 35 million tests per day, or more, to include daily testing of front-line workers...

“Without ubiquitous testing — testing everyone with symptoms, and those they have come in contact with — we simply cannot be confident that a reported decline in cases represents a true decline in infections – and that it’s safe to open,” explained Ashish Jha, faculty director of Harvard Global Health Institute, or HGHI, and a co-author of the group’s estimates, in a Time editorial. “If a state misjudges its true underlying infection trajectory, it may suffer large flare-ups of the disease, necessitating a long and painful lockdown again.”...

Two other groups, also adopting a contact tracing strategy, offer other testing benchmarks. The Rockefeller Foundation suggests an initial 3 million tests per week, or about 430,000 tests per day, by mid-June, then growing that number 10-fold over another six months...

If contact tracing is not part of the equation, even more tests are needed because the approach becomes an untargeted national surveillance method...
Other scientists are pessimistic that contact tracing will work in the U.S., especially if case numbers remain high.
“It’s clear that you can do a lot of control if you do contact tracing really well. Singapore managed with mainly contact tracing for several months,” said Marc Lipsitch, an epidemiologist at Harvard University, in a call with reporters. “But then eventually even Singapore lost its control of the epidemic and had to resort to social distancing types of measures.”
“In conjunction with really aggressive measures to get case numbers down — and significant resources — contact tracing can be a useful piece of the control approach,” he added. “But I think it’s very challenging with an ongoing epidemic.”...
https://www.factcheck.org/2020/05/how-many-covid-19-tests-are-needed-to-reopen/