After they get the website fixed, then what? Keeping your doctors and hospitals may be the next vexing challenge for Americans in the new health plans created by President Barack Obama's law. Obama promised people could keep their doctors. But in many states the new plans appear to offer a narrow choice of hospitals and doctors. Overall, it's shaping up as less choice than what people get through Medicare or employer-based coverage. Also, it can get complicated tracking down which medical providers are in what plans.