The science, the actual hard number for mortality rate, is very low. It is the anecdotal evidence that is terrifying everyone (the terrible way in which it kills when it does kill, and the rate at which it spreads).
I am personally not afraid of it, I wear a mask out of courtesy and not wanting to spread it if I happen to be one of the silent carriers.
I've best seen it described by a mathametician as follows (wish I could find the link) - COVID-19 has comparable mortality to the flu, but you are 300 times more likely to contract it.
For something with such a low mortality rate I do not support mandatory contact tracking or testing. I certainly would if the number starts sharply going in the other direction.
I can't say for sure what will be pointed out specifically about socialized medicine in the UK, France, and Italy, but our numbers for the United States outside of NYC appear to be much better than those countries and I suspect that is where the right wing will come out and say our private system outperformed the public systems (i.e., cherry picking the countries with the highest mortalities for comparison with the US).
They will point out that Italy had to triage beds and favored treating younger patients with higher chances of survival, allowing some older patients to die. It was the rational thing to do, but also unimaginable here in the US where you would be sued to high heaven.
Can't you imagine the situation in Italy turned into a campaign add in Florida? "The Democrats want a health care system that lets seniors die" or some such with some pictures of overwhelmed Italian hospitals and a sad looking old man not being treated, but coughing and wheezing.
I never said these were good arguments, I just know that they will say it, I've been following politics for a very long time.
The only crises that bring both parties together are ones that hit everyone. Technically a virus hits everyone (does not discriminate as you say), but in fact it does discriminate. It spreads faster where population is denser and where there is mass transit.
So just like everything in the US, this crisis is divided between urban and fly over. The urban people are literally worried for their lives, and the fly over people are worried about their jobs. This is a super broad generalization, but I am trying to make the point that the virus is not affecting all people the same way and it happens to be right down party lines.