As mentioned earlier, your example requires a "stage direction". Anyway the issue becomes interesting when this is not in the gap, but before (or after) it. When we have to rely on a sign. Like in Kate Gregory's example:
Only a few words could come out a a time. "I want to be ... the president."
But there the three dots are, in my opinion, not the appropriate solution. Three dots are for me a less forced pause. More a pause for thought:
"What do you want to be when you grow up." She looks up at the stars and answers quietly. "I want to be ... the president."
In the gasping case, I'd prefer the hyphen.
Only a few words could come out a a time. "I want to be — the president."
By the way, same if the sentence breaks off in conversation.
"Honey, let me —"
"I don't want to hear."
"Please. I was just there to —"
"You were there to meet her. And then you —"
"Stop! That's not true."
Chosen interruption / fadeout:
"I love you. You are my ... greatest treasure. I ..."
He listens to her while she continues speaking.
"I ... I don't ... I don't know how to say it."