Currently, there is no federal law addressing the process for dealing with emergencies on Election Day. Some state laws provide guidance for Election Day emergencies, however. Generally, these laws outline procedures for postponing or suspending elections. The most common statutory approach is to permit delaying the election, changing polling place locations, or doing both. A state-by-state chart is shown here.
California, Florida, Oklahoma, and Virginia have the most expansive emergency election statutes. Most emergency statutes require unilateral executive action, meaning the governor is given the power to delay or postpone an election. Several states require either direct gubernatorial involvement or consultation with the executive branch in an election emergency (Florida, Kentucky, Louisiana, Maryland, Oregon, South Carolina, Texas, Virginia, Utah, Illinois, and Maine). Under these state law regimes, therefore, it seems the governor has significant power to delay or postpone elections based on either a direct statutory grant of power or indirectly by declaring a state of emergency.
New York has a unique statute that allows for another day of voting not more than 20 days after the original election day if an emergency causes fewer than 25 percent of registered voters to show up to vote. NY CLS Elec. § 3-108.
Events that can trigger emergency statutory provisions include public health crises, floods, hurricanes, earthquakes, fires, power outages, active shooter situations, cyberattacks, or any number of other “emergencies.” Most statutes define “emergency” broadly, and states likely have significant power to manufacture emergencies based on Covid-19 or anything that might reasonably be termed an emergency. However, they would need unilateral support from the state executive branch, and under most state laws would need to provide an alternative mechanism for voting.
Whether a state law that authorizes a state official to change the day on which an election is held conflicts with federal law (3 USC § 1) is an open question. It is possible that such a law would be interested as an application of 3 USC § 2, and be deemed the alternative procedure for selecting electors because of that “failure.”