Under the FMLA, you are required to give your employer certain reasonable notice of the intent to take such leave. However, the law does allow for shorter periods of notice if there are certain emergency situations that prevent you from making earlier requests. Your facts do not disclose why you waited to the very last minute to ask for the leave.
You should consult with an attorney that is well-versed in FMLA law to determine if your situation allowed for you to give very little notice, and what remedies are available to you, if any. At that time you can share all of the facts and circumstances with the attorney.
Good luck to you.
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If you are taking FMLA for baby bonding, it seems that you would have been able to give your employer more notice. If your child has a serious illness and you needed to care for her on an emergency basis, it would appear that your employer may violate your rights if they terminate your employment. More facts need to be known. I suggest that you try to work with your employer in giving them reasonable notice and then taking your bonding leave. If you get fired or retaliated against because of the FMLA issue, call an employment law attorney.