No, not really. As far as I can tell, political affiliation actually has NO bearing on how worse or better the cases are. At least, state-wise.
Densely filled population is the main issue and hit hits Red and Blue states equally. In the top ten of both cases and deaths, there are roughly half Red states and half Blue states... In fact, rurally speaking, most of the country is red but the cities were hit the most and they tended to vote Blue. So, saying the Democratic governors and mayors handled it poorly based on that data is valid, but only in so far as the number of cases and deaths.
Whether or not the shut downs are helping or not will take time to know the full ramifications.
I'm by no means arguing that there shouldn't be shut downs, only that their argument so far has been adequate in regards to Democratic governors and mayors having the hardest time with this. Only, in that regards.