I don’t think the problem is that he is missing these deadlines.
I think he has a real problem in estimating the amount of time it will take to complete a task.
Have him start keeping a journal of what he says a task will take and how long it actually took him to complete the task. Eventually, this journal will become a sort of guide for him to create better estimates. Once he becomes better at estimating, he shouldn’t feel as rushed or harried.