Just in from Pew Research:
As a growing number of states ease stay-at-home restrictions imposed in response to the outbreak of the novel coronavirus, a majority of Americans (61%) say it is primarily the federal government’s responsibility to make sure there are enough COVID-19 tests in order to safely lift the restrictions. Fewer (37%) say it is mainly the responsibility of state governments to ensure there is an adequate supply of tests.
Partisans differ sharply over which level of government bears the responsibility for COVID-tests: A sizable majority of Democrats and Democratic-leaning independents (78%) say this responsibility primarily falls on the federal government, with 28% saying it is entirely responsible for making sure there are enough tests. A smaller majority of Republicans and Republican leaners (57%) say this is primarily the responsibility of state governments.