One of the most typical career questions I get is from recent college grads who are at the bottom of the totem poke. Often, they have two or more senior colleagues who delegate work to them. Unfortunately, there simply aren’t enough hours in the day to do everything, and they find that they’re either saying no to someone all the time, or they’re working until they drop.
This is a tough situation, because you want to be perceived as a can-do, enthusiastic employee and should therefore try to avoid actually uttering the word “No” to anyone you work with. However, you have to be mindful of your own stress level and sanity too.
I recommend trying to pre-empt situations in which you will have to decline an assignment, specifically by formalizing your daily responsibilities with your official boss. Talk to your boss about who on the team is authorized to delegate work to you and note the type of assignments you can expect from each person.
If one of your managers comes to you with an assignment but your time is already accounted for, tell that manager that you wish you could help, but you are working on another project that requires your attention. Either you can go to your boss directly and ask him which task you should prioritize, or you can give the manager the option of speaking to your boss about it herself.
Remember to stress how much you enjoy working with this manager, because you want her to leave with the perception that you really do want to do the task and can’t help being caught between conflicting responsibilities. In a nutshell: get your boss to say “no” for you and keep yourself looking good to everyone!