Steering wheel does not turn the tires

This isn't something I've heard of, but it sounds like there's going to be some serious lawsuits involved if you can lose the steering while you're driving. In the past, if the engine stalls while you're driving, you will lose the power steering assist, but there is always a mechanical back-up. You'll need muscles to turn the steering wheel, and the effort needed will get progressively harder and harder the slower the car goes. You will usually also lose the power brakes, but again, there is always the base brake system that still works. Depending on the system used in your car, you could get as little as two power-assisted pedal applications, or many more, as long as the ignition switch is still on. There's enough power assist reserve built in to allow you to stop the car in a safe, controlled manner.

Within the last few years, the manufacturers are going to a self-contained power steering system that doesn't use a belt-driven power steering pump and reservoir. To my knowledge, they still have a mechanical back-up like they always have had, so you shouldn't be able to spin the steering wheel freely. Regardless, the thing to do is return to the dealer that sold you the car and tell them about the problem. Typically, if they can't make the problem occur, they won't know where to start looking for the diagnosis, but as long as you have the problem documented on the repair order, the manufacturer will usually take care of it under warranty, even if the car has gone out-of-warranty.