You can't just fail to show up for work one day and then excuse it with the Family and Medical Leave Act. You must provide a written request for such leave. When it's possible, you must give 30 days notice before starting the leave. If your wife is pregnant, it's not a good idea to wait until the ninth month to announce that you want to take some time off. The employer can make you wait the required 30 days before you can take leave.
Illnesses are harder to plan.
In certain circumstances, you can take leave immediately, or within one to two working days. When requesting leave, the employer has the right to require medical certifications. Just one doctor's note may not work. The employer can request second and third medical opinions, but the employer must pay for those. The employer must also continue to pay the employee's group health benefits during leave.