You said that you work through an employment agency. Does that mean you work as a contractor? Is it a temp agency, or do you work for the employment agency itself. If your employer(the company that signs your paychecks) has a human resources department, I would contact them regarding FMLA(Family Leave Act) and tell them you need time off for personal reasons. You can get a doctor's note without specifying what your specific condition is...no reason that your employer has to know that it is stress related.
If you go through Human Resources, it is much easier than going directly to your boss, and HR is not supposed to fill in your boss as to why that you need time off, just that you will be gone for a period of time. If you tell your boss you are stressed out and need time off, he can just fire you if he has a mind to do so. Most states these days are "at will" employment states. That means they can fire you "at will" without any grounds at all and there's nothing you can do about it. Occasionally, people try to sue, but rarely do they win.
If you do take the Family Leave, there is still no guarantee that the same job will be waiting for you when you return. The employer can move someone into your job slot, and stick you somewhere else when you come back. I'm not sure any of this is helping out, but if at all possible, release as little personal information about yourself as you can get away with.
Please let us know what you decide to do. Good luck.