Mission Impossible.

This year it has been more than the title of a popular movie or long-running TV series, say those tasked with collecting data for the U.S. Census Bureau.

Census enumerators have dealt with shifting counting deadlines, uncooperative respondents, a revolving door of supervisors, spotty cell phone service, unmarked addresses and hazardous roadway conditions – all while navigating a once-in-a-century pandemic.

“Every enumerator I talked to agreed in 10 years there would have to be major changes in the way a census is conducted organizationally and in terms of safety,...