This section from NYCL is a local example of what powers an executive may be allowed to exercise when he or she declares a state of emergency, and under what circumstances and limits.
In short, it allows executives to perform acts they are not normally authorized to do, bypassing procedural requirements for certain acts and performing certain denials of liberties that would normally be protected.
These include, for example, 1(a) “the establishment of a curfew and the prohibition and control of pedestrian and vehicular traffic, except essential emergency vehicles and personnel;” 1(b) “the designation of specific zones within which the occupancy and use of buildings and the ingress and egress of vehicles and persons may be prohibited or regulated.”
I’m assuming the authority is derived from the police powers. I’m not sure if they have explicit authority to override certain rights or executive privilege (including the executive right to constitutional interpretation) and separation of powers. Presumably, certain acts would be so unconstitutional that the courts might act.
Korematsu v. United States, 323 U.S. 214 (1944) demonstrates courts deferring to the executive for the above reasons. And yet, that same day the Court decided in favor of a plaintiff in a similar case. Also, I’m not sure the Court would rule the same way as in Korematsu today.
That said, courts will observe deference to executive use of emergency powers. But, again, that’s not to say they can’t be challenged. An example in that vein would be Harry Truman’s failed attempt to seize steel mills and production during the Korean War (Youngstown Sheet & Tube Co. et al. v. Sawyer.) And yet, “although the Court found the president’s actions to be unconstitutional, its decision did not signify a triumph of private rights or a significant check on the government’s exercise of de facto emergency powers.” https://www.independent.org/publications/article.asp?id=1394
