St. Louis has been battered by two tornadoes in the past two months. A fire shut down a new nursing home last month in Enterprise, Ala., forcing residents to evacuate. Cleveland grappled with a power outage while inundated with visitors for the N.C.A.A. women’s basketball Final Four.

In each case, local health officials played a key role in containing the fallout, assisting hospitals, finding new homes for displaced residents, and coordinating efforts with fire, police and other city departments.

The funding for this work, about $735 million in total, comes from the Centers for Disease Control and Prevention. In President Trump’s proposed budget, the money has been zeroed out.

The proposed cut has left health officials increasingly alarmed, particularly since it followed $12 billion in cuts to state and local health departments in March. Nineteen states and the District of Columbia have sued to prevent the reductions.

“Man-made and natural disasters don’t depend on federal funding, but a response to save lives does,” said Dr. Matifadza Hlatshwayo Davis, health director for St. Louis. (Dr. Davis has resigned but is staying on until the city finds a replacement.)

The city is coping with huge sinkholes, routinely faces floods, and sits on a fault line that puts it at risk of earthquakes. “We really rely heavily on this funding,” Dr. Davis said. Without it, “the entire population of St. Louis and its visitors would be left vulnerable.”