Can you point to your deadline? In this moment, does it exist in anything other than a symbolic form? Then from where does your stress arise: time or your thoughts about time?
Sundays feel differently than Fridays but is there actually a quantitative difference between those days? We imagine a difference and then live with the feeling of that imagination.
The question is not whether or not time is an illusion. The question is whether or not time is an illusion for you. The illusions we live with seem very real, otherwise there would be no need to point out that they are unreal.
Time is an idea we use in order to be able to plan and produce complex things. But when you start living in your idea of time, you create suffering for yourself such as stress and fear.
Daily meditation will help make this obvious to you. I would also recommend the book The Power of Now by Eckhart Tolle.