Feeling overwhelmed often happens when a task seems too big to conquer. Many years ago, a mentor asked me this question, "How do you eat an elephant?" The answer is, "One bite at a time." The point he was making is that if you can break seemingly large tasks into smaller (less intimidating) pieces, eventually you will be able to eat that elephant! Yours may be a simple case of not taking on anymore responsibility than you feel comfortable with. That may mean that you don't attend every meeting, or participate in every each even that your organizations hosts. It doesn't mean that you're any less passionate or any less of an asset to any organization you are a part of. You may simply need to re-allocate your time.
I will also offer you this. It is better to hold a leadership position in a single organization than it is to be a member of several organizations. Your leadership experience will have a far greater impact on your application than a list of all the clubs you've ever been a part of. If there is an organization about which you feel particularly strong, give it your all and don't be afraid to let the other ones go. A position of leadership will likely require a significant amount of time so even though you may only be involved in one organization, you may find that you're putting in just as much (or more) time than if you were involved in multiple extracurricular activities. I hope this is helpful. Best of luck. You're already ahead of the game.