Usually not. 

The Family and Medical Leave Act (FMLA) requires employers to allow a leave of absence for serious health conditions. You may be eligible for FMLA if your company has 50 or more employees, and you have worked there for at least 1 year. Under FMLA, the employer cannot deny you leave simply because it is inconvenient for them. Doing so is illegal 'interference' with your FMLA rights. 

For more information on FMLA rules and rights, you can consult our FMLA page.