HARVEY, Ill.—Christopher Clark was elected mayor last year, pledging to seek business tax reductions and lower water bills. They were popular goals that seemed in reach given that city revenues had been rising almost every year since the recession.

On taking office, Mr. Clark quickly figured out the city’s progress had stalled. Property tax collections were down, and businesses were cutting jobs. A fall in city revenue, coupled with growing debt payments, meant there would be no relief from business taxes or water bills.

“We just have to figure out ways to do more with less,” Mr. Clark said, echoing a familiar mantra surfacing in dozens of U.S. cities.

A decade of growth in the U.S. economy allowed cities to patch fiscal holes left by the financial crisis and recession. A surprising number now see new signs of trouble.

The proportion of American cities expecting general-fund revenue to drop more than 3% when the books close on the 2019 fiscal year increased to 27% from 17% in fiscal 2018, when adjusted for inflation. That is one of the findings from a Wall Street Journal analysis of data collected from 478 U.S. municipalities by the National League of Cities, an advocacy group.