Can my Illinois employer search my car in suspicion of drug use?

I have been employed with a privately ownder nursing home for approx. three years. Recently my administrator and DON have created a new drug policy that states that if they have any reason to suspect drug use, they can search you and your personal belongings as well as you vehicle. Any refusal to comply will result in termination. I understand searching me and my bag, but I'm not comfortable with the fact that they can search my car just because someone says, "Oh yeah, Nikki smokes crack" (which i don't, btw) I also don't agree that they can change and modify this policy at any time without giving notice or obtaining new consent. If i fail to agree to this policy and don't sign it, I will be terminated. Can someone tell me if they have the authority to do this three years after employment and if my personal rights are being violated?