The volume of medical data being created and published is rapidly increasing, and it would take a doctor to read something like 160 hours per week to stay on top of their field. There are only 168 hours in a week, so there is really no way a doctor today can keep up with what is going on . The idea of Watson is to be able to take large amounts of unstructured data (i.e. an entire patient history and current symptoms) and be able to find a solution. I don't think Watson will replace a doctor or physical interaction anytime soon, but a device connected to Watson or similar solution will most definitely be used to augment the doctor's diagnosis and treatment solution.
Watson might be able to partially replace some specialists that primary care physicians use for consultations. When PCPs are unsure about a diagnosis or proper plan of care they will often consult with a specialist for advice via phone or e-mail. So in that case the PCP has already gathered at least some preliminary data and could feed it to a computer. But even for that use case Watson won't be able to provide same level of back-and-forth interaction that's often necessary to achieve the correct result.