First: discuss with your development team the issue, make sure you get buy-in on replying to management with one voice. A.K.A.: avoiding you saying "We can't do X" and someone else goes: "Of course we can!". Second: talk to your manager. Don't send an e-mail. That would just turn in a long, and possibly bitter, battle of 're:re:re:re:' or be interpreted as a C.Y.A. fig leaf. Make sure you start by understanding where…
I think this is probably about as close as we will come to a process that would work. I'd say that right now the company I'm working for doesn't have the structure in place - no team leads, for instance - to dissipate the heat when it's on, and no procedure to follow when things go wrong. These are definitely things to think about as we grow. Thanks for the constructive reply!
I always believe in good faith and positive intent - call me naive - so I assume the managers have their own pressure to respond to and business needs to satisfy.
The 'understanding' first step is needed to see if there is an interim solution that takes the fire away from the business, the manager and the dev team. IE: The feature with the bug is not as urgent as other features in the same drop; squirrel away the bug behind a feature flag and deliver the rest. Now you can go ahead and fix the bug with a proper pace.