$10 billion per month is far, far less than either 1) the economic losses of the pandemic to society, or 2) the amount of money the pandemic is costing the government. I have no knowledge on whether it's feasible, but if it significantly reduced the impact of the pandemic, the economic decision is easy.
"could we manufacture 10 billion of them a month?"
Yes, it could be done.
According to that TWiV episode (which, again, I encourage everyone to listen to) the tests are very simple: just a piece of paper with some antibodies on it.
As for the $10 billion per month cost, from the TWiV episode (about 31 minutes in):
It just boggles my mind, the enormity of this problem. This is killing enormous numbers of people every day. It's costing the country trillions -- literally trillions of dollars. This should just be part of the national emergency.
It's one thing to make vaccines, it's one thing to make therapeutics, but these are things that necessarily take time. We have to wait to see what the efficacy is, we have to... it's really hard to make therapeutics. A diagnostic test should be a no-brainer. Make a $1 test. Get it to everyone. Change the way we view these things, and that should be completely being plowed through by the federal government.
We don't have to make 300 million of them overnight. We just have to focus them at the moment in places where the cases are worst... it's just astounding that we don't see a flurry of activity from the US Army...
I don't know who makes it, but take every manufacturing company that knows how to print paper, adapt their tools to print monocolonal antibodies on to those sheets and just start slicing it up and shipping it out. It's as easy as that.. well, you know, I'm simplifying it a bit but...
And could we manufacture 10 billion of them a month?