I would say you have a right to know why a bug needs to be fixed at 'close-of-business'. You just have to try and ask it in an indirect and non confrontational

I would say you have a right to know why a bug needs to be fixed at 'close-of-business'. You just have to try and ask it in an indirect and non confrontational way. This will better help you determine a practical and pragmatic approach because you will have a better understanding of how serious the issue actually is and it's implications may be simply overstated or exaggerated as most shitty managers are known to do without consideration of the stress and harm it may cause to others. In any case I would try to push early that we need two plans, one for a solution and one without. Try and manage expectations as early as possible by making the possibility of no solution viable in their thinking. If you feel they are unresponsive or unwilling to accommodate a reasoned approach then as others have said maybe better to be fired - does not seem like a healthy environment.