SACRAMENTO, Calif.—In making their case for California’s policies on climate and immigration, Democrats proudly note the state’s status as one of the world’s most powerful economies, driven by thriving tech and creative industries.

Republicans here are pointing to a different metric: the poverty rate.

“Poverty is the No. 1 issue for California.… We have to work to fix it,” said Republican state Assembly leader Chad Mayes. “It is directly related to the policies we have put in place in California.”