It means "don't look forward to it". One more Ex: She said she'd get back to us, but don't hold your breath!
2018년 1월 1일
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I would say it's closer to "Don't expect that to happen". So if you're hoping your best friend will visit you but they're very very busy, someone might tell you "Don't hold your breath", meaning "Don't expect your friend to come over".
2018년 1월 1일
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It's basically like saying, "I wouldn't count on it."