Welcome to software engineering. I am only partially joking. These types of situations are not uncommon and can actually work out to your benefit if you can t

Welcome to software engineering. I am only partially joking. These types of situations are not uncommon and can actually work out to your benefit if you can take advantage of it. Your new boss told you to say no more often, he/she is giving you a lifeline and you are saying you're scared to take it? Instead of a direct no try saying it as, "I really would like to work on your issue and you have expressed its importance but I am limited in how much I can accomplish and right now my schedule is full. I may be able to get to it in X time period, but I can't make any promises today. However, if you'd like to have this prioritized then you can feel free to speak with Mr X who is my boss." And then you document the details either just to yourself, or you can send a heads up email to your boss. This happens a lot in companies of all sizes, people make requests of engineers (generally young/new ones) and see just how much they can sneak around the system. One of the most important skills as you mature in your career is to say no. Saying "no" but getting your work done will not get your fired, saying "yes" and failing to keep up on your work will. Think of it this way, if these are higher level people then you that are making requests and their compliant about you is you said no because your schedule is full, it really won't go too far. If instead their compliant is you told them yes and then you never did it, their complaint will be valid.