SANTA RITA, Venezuela—Sara Meza is just the kind of voter Venezuela’s opposition could once count on at the ballot box.

A 32-year-old teacher, she’s fed up with President Nicolás Maduro’s government. Her salary has fallen to the equivalent of $2 a month with Venezuela’s currency collapse. She struggles to feed her 10-year-old son and is unable to treat the small tumor on her breast because the health-care system is in shambles.

Still,...