Becerra's mother was born in Mexico, coming to the U.S. after marrying his father, and he said she likely would have been affected by the policy. However, the rules don't apply to U.S. citizens, even if the citizen is related to an immigrant who is affected.
Many immigrants are ineligible for public benefits because of their status, and an Associated Press analysis found low-income immigrants use Medicaid, food aid, cash assistance and Supplemental Security Income, or SSI, at a lower rate than comparable low-income native-born adults.
Those who work with immigrants say the rule, which doesn't go into effect until October, is already having a negative impact. California counties administer the food stamp program and Medi-Cal in the state.
"The data are hard to tease out, but we have heard, for about two years now, every time there's been coverage of a possible rule coming forward, people will call and they will say please remove me from the rolls. Or please withdraw that application that I had filed," said Cathy Senderling-McDonald, deputy executive director of the County Welfare Directors Association of California.
Trump's attempts to thwart illegal immigration have drawn the most attention, but the latest announcement Monday affects people who entered the United States legally and are seeking permanent status.
"We want to see people coming to this country who are self-sufficient," said Ken Cuccinelli, the acting director of Citizenship and Immigration Services.
KQED's Katie Orr contributed reporting to this story.