Hi Sergiy,
Deadlines are different than estimates, in my opinion. We often get fixed dates because, as you say, regulations or maybe laws have changed, making it mandatory to have a change done by a specific date.

We often lie about whether we can meet the deadline because we feel the pressure to say we can deliver all functionality by that time because of coercion.

In reality, what we should do is to accept the deadline and find out what is the absolute minimum required functionality required at the deadline. Whether or not you can meet a deadline or not is more often about planning than estimates. That is how far in advance you get to know about the deadline.

In most cases, you have a gut feeling about whether you can do it or not. Science has proven that rough estimates, such as planning poker, give as accurate (or inaccurate) estimates as careful analysis when complexity is high.

When you have a deadline, it is even more apparent that your time is fixed. You can choose to throw in more people, but then Brook’s law comes into play “Adding manpower to a late software project makes it later.” So the only thing that is variable is the scope. So what you have to do is to slice the scope like a carpaccio to find the absolute minimum requirements and work from there. Again, you don’t need estimates to do that