There is an idiom "hold one's breath", and it basically means "be anxious, worried or excited (about something" or "be in an anxious, worried or excited state of anticipation (about something)". The expression refers to the fact that normal breathing can be interrupted when someone is in such a state (anxious, worried or excited).
So, you might reword the sentence this way: "
Everyone in the world is anxiously waiting to see how Americans vote."
EDIT:
Oops! I'm far too slow for GG.