What US laws currently impede the fight against COVID-19?
It is not that such laws impede (that is, ex-ante) the fight against coronavirus. Instead, prosecution for not abiding by those laws under circumstances of emergency would lead to the absurd outcome of penalizing (ex-post) people's efforts toward stopping the spread of the virus. Thus, it is a matter of balancing the competing interests of constitutional/statutory freedoms on the one side, and public policy or the common good on the other side.
As an example, consider the US government's likely decision to restrict or prohibit interstate travel. This prohibition seems justifiable as an attempt to curb the spread of the virus.
An infected person could complain in terms of U.S. v. Guest, 383 US 745, 758 (1966) ("freedom to travel throughout the United States has long been recognized as a basic right under the Constitution", citing cases). However, leaving that person's freedom of movement unaltered exposes the population of the destination [virus-free] state(s) to a high risk of contagion, which is precisely what the government intended to prevent.
Most examples have to do with the freedom of movement. In addition to that, any form of quarantine or a prohibition to attend gatherings might also be construed as a hindrance to people's freedom of expression or their right to assemble as premised on the First Amendment. The rationale is inline with the argument that "people can engage in effective speech only when they join others". But, similar to the previous example, the risk and impact of contagion are too high to preserve or remedy the person's said rights under a situation that can easily get --or might already be getting-- out of control.
Note: This is not intended to be an exhaustive answer.