When Larisa Casillas gave birth to a boy two years ago, the Bay Area nonprofit organization where she worked gave her only four weeks of paid leave. But she took more than that, including 12 weeks paid by California’s state family leave program, one of the few of its kind in the nation.

Ms. Casillas said the extra time was essential for bonding with her son, meeting other mothers and staving off postpartum depression. “Honestly, without that income support, I wouldn’t have made it,” she said.

If President Obama has his way, paid leave for new parents and people caring for ailing relatives will become national policy. Last month, he gave federal employees the right to take six weeks of paid leave when they become parents. And in his State of the Union address, Mr. Obama framed paid leave as a crucial economic matter.

“It’s time we stop treating child care as a side issue or a women’s issue, and treat it like the national economic priority that it is,” he said. Paid leave could help increase the percentage of women in the work force, he said, and help middle-class families earn stable incomes.