I don't think testing for this is actually that hard or that hard to scale - we had the full virus sequenced and its genome up on the internet within a couple weeks. Initially we do pcr based tests (easiest to "develop" - you just find the right primers which takes a couple more nites and then maybe a week or two to make sure it works). And there's already talk of people using new tools like SHERLOCK (CRISPR based diagnostics tool, and other tools like LAMP could be used as well (it's a special type of very fast, very sensitive pcr) since I recall some work done with LAMP in previous coronavirus outbreaks. One thing potentially making it hard is just getting equipment/kits into shut down cities (see article discussing Roche's diagnostics effort linked below). There are definitely challenges, but in diagnostics, the technology has come a long way to allow cheap, rapid, scalable testing.
Roche: https://www.bloomberg.com/amp/news/articles/2020-01-30/roche...
LAMP: https://virologyj.biomedcentral.com/articles/10.1186/1743-42...