In Michigan, some unstaffed highway rest stops are shuttered. In Santa Barbara, Calif., local librarians are out of a job. Dayton, Ohio, has ordered furloughs at nearly every agency, and in Arlington, Tex., police officers and firefighters may soon see painful cuts…

Among municipalities, the new budget cuts could be profound: Between 300,000 and 1 million public-sector workers could soon be out of a job or sent home without pay, according to a new estimate from the National League of Cities. The steep reductions in staffing levels could affect education, sanitation, safety and health, local leaders warn, potentially leaving critical public services in utter disarray.

For governors, mayors and other top local officials, their economic troubles stem from the precipitous drops in revenue that have come as a result of shuttered businesses and sharp decreases in shopping and travel. The extent of the disruptions are poised to reach a level not seen since the Great Recession more than a decade ago, a reality that has prompted many city and state leaders to plead with Washington for help.