I'm probably too late to answer this one... But as someone who has made some big workplace mistakes, this is what helped me the most.

I wrote a sincere personal letter to my boss when I made a particularly bad error. I explained the error, what led me to it, and how I intended to change my practices to avoid the error in the future. It helped me feel a little better to put everything out there, and my boss was pleased to have an explanation for what went wrong, as well as a plan in place to prevent such missteps in the future.

I'm sorry you're in this position, though, and hope everything works out! That sounds like a high pressure job!