The law you're referring to is known as the Family and Medical Leave Act (FMLA). It entitles you to take up to 12 weeks of unpaid leave to care for your new child, but only if you work for a covered employer and meet certain eligibility criteria. Under this law, while you're on leave, your employer-sponsored health insurance benefits are protected, and your employer must return you to the same job or a similar job when you come back to work.

You may be covered under the FMLA if:

• You work for a private company that has 50 or more employees, or you work for a public school or agency that has less than 50 employees, and
• You have worked at least 12 months (not necessarily consecutively) for that employer, and you have worked at least 1,250 hours during the 12 months immediately preceding your FMLA leave start date

Even if you are covered by the FMLA, your employer can require you to use any vacation days, sick days, or personal days you've accumulated in place of unpaid leave time. For instance, if you've accumulated two weeks of vacation time, your employer can ask you to use those weeks first, before giving you an additional 10 weeks of unpaid leave. You're also required to give your employer at least 30 days' notice of your need for leave, or as much notice as possible, depending on the circumstances.

You should also check the rules of your state, because some states have their own parental leave rules and may pay disability benefits to new mothers. However, if you're not covered by any law, there's not much you can do. Unless you can negotiate more leave time with your employer, you'll either have to go back to work after six weeks or face losing your job.