Meeting deadlines is important, but most important is to be able to anticipate delays in any project. If for whatever reason some employee is requested to deliver a report with a given deadline, 2 things may happen: 1) he delivers it on time, 2) he doesn't
The problem is not that he didn't deliver the report on time. The problem is that he creates uncertainty about any future deadline if he consistently fails. Failing to deliver a report on time may be due to several reasons. If that person is truely a good performer the problem may be that he accepts workload and deadlines that he cannot possibly accomplish. It's much better to develop a culture of honesty where bosses request deadlines that are compelling but achievable and employees are honest about what they can do and cannot. In the worst case, if there is open communication between both of them, they will work out any difficulties to accomplish their objectives.
I haven't seen this type of honest communication very often and this terribly hurts companies. Employees and bosses not only get frustrated, but it also impacts trust, which is key to deliver good results.
My recommendation: promote honest communication. If you are a boss, always try to figure out if your requests are realistic and open communication channels with your employees. Promote trust. If you are the employees, provide honest feedback to your boss is the deadlines are not realistic and avoid surprises and uncertainty.