Actually the way the sign up process works is you will only be able to sign up once per year so if the illness needs to be treated immediately like a broken leg you will not be able to buy insurance until the next open enrollment with coverage not starting until January of the following year.
I have no doubt that Obama will see the “unfairness” in this and allow people to sign-up at anytime.
I mean, he has done it so far with everything else in the law, so why wouldn’t he just wave his hand and make it so?