Found a set of winter tires 205 55 16 for great price. Have 205 60 16 on the car now. 2004 Chrysler Sebring. Will these be ok to use without causing any problems?

 

The lower profile will mean that the rolling radius is a little smaller. This will slightly affect your speedometer and odometer accuracy. You'll actually be going a little slower than you read in the car. Your actual gas mileage will probably go down a little, but you won't be able to tell because the odometer will be off. If you have access to a GPS unit, you could check this out.
The car will ride a little lower and the ride might be a little bit harsher. The bottom of the car will be a little closer to the ground meaning that you might get stuck in deep snow a little sooner than with the taller tires.
There aren't any large effects, but the car was designed to operate with a certain size tire so things will be a little different.