Under the Family Medical Leave Act, a mother or father can take 12 weeks of unpaid leave to care for a sick child. But, the FMLA does not apply to employers with less than 50 workers and it does not apply to part-time workers. The FMLA has limits. It does not apply to many workers. Actual paid parental leave is even more rare. Only some 12% of American employees work for a company that offers paid parental leave.
Unfortunately, when compared to other countries, the USA is way behind. Huffington Post has produced a handy chart that shows the disparity. See the Huffington Post here. In fact, just looking at maternity leave, the USA rates as the worst in the world, tied with Lesotho and Swaziland. Wow.