I know since Tuesday morning that we will need to complete assignments A, B & C by Friday. Normally all three would require the full working days from Tuesday to Friday - so we start working on those tasks.
On Wednesday morning, we find out that we also need to deliver X & Y on Friday, as well as Z on Thursday (same work duration). These have higher priority than A, B & C, but our deadline on A, B & C doesn't change - we have to deliver all six assignments anyway.
What we have done so far is deliver all six by staying up all night. However, this keeps happening more and more regularly and I (and those who report to me, whom I delegate all this work) get to a point where working overtime just leads to tiredness, pains and mistakes.
In other words, even if we manage to do all six, the quality is sometimes considerably lower than if I/we had worked while being fully rested, awake and focused.
Would it come across as professional, proactive and positive/accountable to explain to my managers that working overtime will lead to bad quality and human error, whereas resting and working while focused will lead to much better quality?
Note when I am talking about "internal" deadlines I mean those set by the department for itself, rather than assignments required by client needs or the overall company.