The reality is that at the end of every workday, there is always work left undone. I have never gotten through every email or every tasker I write in my notepad, and I think most people are likely in the same situation. We are fooling ourselves if we think we'll wake up one day and literally have nothing to do.
So when we have work and delegate it to our subordinates (or have it delegated to us by our boss), the refrain of "I'm too busy to do it." is simply an excuse. You're not too busy, you've simply prioritized something else above it. Maybe that task is higher priority, but often what I find is that there are lots of tasks that suck up our time and aren't worth it.
I found one division having new check-ins print a multitude of training certificates and hand walk them to an office so they can be punched into FLTMPS. One of my petty officers used an online drop box so that we didn't have to print the paper in the future, and on top of that anytime a Sailor added something to the dropbox, he got an email so he knew exactly when to log in to enter data. We saved over 800 sheets of paper and countless man hours. Now that he is no longer busy with that, he has more time to spend on Sailor issues and streamlining other training.
If you catch yourself saying "I'm too busy" to your boss, try this experiment. Put on your Outlook calendar (or paper if you don't use Outlook) 10 minutes at the end of the day to total up what you spent your time on. At the end of the week, total the time, then look at your command's guidance. You'll likely find a massive mismatch between what your priorities should be and what you spend your time on (and what you actually spend time on IS your priority). I found I was spending a LOT of time traveling between buildings. I reworked it so that whenever I went to a building I spent at least 2 hours and walked in prepared to take care of a lot of business. It saved me time and I spent more time on projects and less time in the car. I've done the same thing at home and found I spent too much time on Facebook, so I consciously spent more time reading books and less time on Facebook. Now I'm getting more reading done, and I find I'm not really missing anything on Facebook.
Busyness is an excuse. Likely you are busy, but not actually matching your priorities with where your time is spent. Figure that out now and watch how your busyness turns in effectiveness.
This post inspired by: http://navycaptain-therealnavy.blogspot.com/2014/03/fighting-good-fight.html