The importance of breathing when speaking publicly is clearly demonstrated in the well known video of ABC News Correspondent, Dan Harris, having a meltdown on national TV. Mr. Harris has bravely and generously shared his fail with ABC in the video link below (see the 56 sec mark for the beginning of the end of his reportorial composure.)
You can tell he is in trouble when you hear the sudden speechless exhale of breath. It is as if the air in his lungs decides to abandon a ship that is starting to take on water. This is followed by additional deflations a few sentences later and that is when the serious foundering begins and the ship sinks. Without breath, speech is unsupported and the body begins to want for oxygen. The voice weakens and becomes unsteady, the head dizzies, the heart starts to work harder, and a rising panic ensues as the mind can't understand why alarm bells are going off and it is losing control. The immediate response is to try to push on, but without the necessary oxygen and force of breath it is a lost cause.
The first and most important thing in this situation is to get your breathing under control, supplying a steady flow of oxygen. You feel helpless because you are robbing yourself of life sustaining breath. Thankfully, Mr. Harris now has a remedy in hand: meditation. The foundation of meditation is, of course, controlled breathing. Controlled breathing is the best triage and the best way to avoid this kind of situation in the first place.
The communication of information requires physical action. In this case, speech. Speech requires breath. Without it the body fails to communicate and starts to implode upon itself. Too much (rapid) breathing can bring on hyperventilation which is also not good. The key is steady, measured, moderated breathing. It is indeed life giving and life saving.
So take a deep breath and then have at it.