Negative consequences are typically seen in lost revenues/margins and budget overruns. In addition: reliability in managing projects is one of todays key differentiator in global industries.
There are many resources (textbooks, good practices, work breakdown structures, project management software packages etc.) out there proposing methods with which to handle the dilemma mentioned above.
A robust and therefore recommended approach to reliably deliver projects is Critical Chain Project Management devised by Dr. Goldratt and his team. It handles the stochastic nature of task durations (Murphy), the psychology of project resources (students behavior) and the adverse effects of heavy multitasking.