1. They probably know less about the issue than you do, including the fact that they don't know what you don't know. 2. The cannot fix the problem themselves; they have to find the best people to fix the problem. 3. They also have managers (or customers) harassing them for answers.
They have two choices. The first is to get the issue fixed as quickly as possible so that they don't need to learn any detail about what the issue really is. If an issue is fixed quickly then everybody cools down and all concerned parties generally become disinterested. The one day deadline is most likely an attempt at option no. 1. The second option for the manager is to find out as much detail about the problem and be confident that they have the best team working on the problem. That way when they have to report to management above them (or to customers) they can do so with relevant information and confidence. Remember, everybody has a boss.
So, now that you know what your manager needs, you need to convince them that they need to follow option no. 2. You need to explain the problem in such a way that they can parrot that information upwards. You need to convince them that you are the best person to do the job. Furthermore, and this is the tricky bit, you need to tell them that you don't know everything but as soon as you find material information you will tell them. After your high level synopsis, swamp them with technical updates. Although these details may not be understood or relevant to your manager they contribute to the trust you need to build up as time passes. If your manager is good and you have been transparent with them they will begin to defend you in higher level meetings.