The original CDC batch became tainted but were more accurate...unfortunately the CDC version was also giving false positives and didn't meet QC. To make matters worse CDC rules required very stringent guidelines for approval from third parties and states. Most of that has been lifted (I think this is what Trump was referring to when he said he was lifting something from the Obama admin, though I don't think it started with him. But who knows because Trump is often full of bluster.)
Here are a few articles about it.
https://www.livescience.com/coronavirus-testing-kits-flawed....
https://www.bbc.com/news/health-51491763
https://www.propublica.org/article/cdc-coronavirus-covid-19-...
I wish people would stop pointing to South Korea and China as the paradigm of how this should be treated. It's entirely possible that the "drive thru" model with relatively inaccurate kits could make things worse. There isn't much point in producing millions of tests if they are no more accurate than a coin flip and can take up to 8 times to properly diagnose someone. Not to say the US hasn't bungled this and wasted some precious time.
The one thing, I'm pretty confused about at this point is how this has spread so quickly in Italy.