I used to go through periods when it was really hard to take the time to process things.
Besides the obvious problem with not processing things, I felt like it weighed on my psyche to know that I had all those unprocessed items.
In other words, I felt like I was falling behind, and NOT getting things done.
Whenever I think I don't have time for processing things, I remember a friend of mine from elementary school whose mom owned a restaurant.
I remember vividly watching her do her bookkeeping at night while watching TV. Because she would spend her whole day cooking and running the restaurant, she didn't have time for that during the day.
Processing is like bookkeeping. As you need to stay on top of your books to run your business, you need to process your inboxes to run your life.
You must find the time, and the best way to do it is to make it so it becomes part of your routine. Just as we always have time to eat, brush our teeth, and watch that one TV show, we need to make "processing" part of that sacred list of tasks we do without thinking.
Here's an interesting article on how to establish a habit:
Processing has become part of my daily life, and I do it constantly.
I know that David Allen says once we start processing our inbox we can't stop until we finish it, but I've found that sometimes I'll open my inbox folder and just process an item or two while I wait on hold on the line, for example. It needs to become second nature.
I hope this helped!