I think emphasis on the former is appropriate because the current measures are reasonably limited to the traditional scope of government disaster relief. Anti-gouging provisions, retooling factories to more socially useful goods, weeks-long shelter in place orders: all of these things regularly happen in response to disasters, although typically not simultaneously everywhere.
I see some people talking about "oh, you know, we'll just have to ban social gatherings until 2021". If that happens - if the official conversation in a few weeks is about extending emergency measures rather than safe strategies for reopening bars - I expect people will get a lot more concerned and diligent.