With a rapidly aging population, the need for the latter will assume increasing importance sooner and more urgently. As of now, the Family and Medical Leave Act (enacted during the Clinton Administration) provides only unpaid leave and a measure of job protection under certain circumstances.
Most corporations provide minimal paid maternity leave (generally about three weeks), which new mothers (or fathers) often supplement with their own accrued vacation time or unpaid leave. The situation is not unlike the American health insurance system as it existed between the post-World War II era and 2010, when the Affordable Care Act went into effect.
In other words, rather than leaving the terms of paid family leave up to businesses (often subject to loopholes and exemptions for smaller firms), making it the law of the land would make paid time off more accessible to more employees.