Depending on where you live in the US, there's already some form of this. Here in Cali it's FMLA, and it's 12 weeks. The purpose of it is to protect your employment while you are out for an extended amount of time, generally for medical purposes (which childbirth falls under). You do not receive full pay, however. I believe it's 60%. There's quite a bit of paperwork to fill out, and you can use vacation time to supplement the pay, if you have it available.
Speaking as someone versed in early childhood development, those 1st few weeks are incredibly important in establishing the bond between parent and child on a social-emotional and cognitive level. Mother and father. This is a good thing. But of course, people with no understanding of the beneficial gain to parents, and particularly to the child, will whine about "their 6 weeks, too".