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You say this when you're too lazy to wait and also too angry to care if the thing ever happens.
You: I won't hold my breath. Your mom: You're still waiting on that pizza? You're still waiting on that pizza?!
Bro: I won't hold my breath. He says that every time he forgets his phone at home.
Mom: I won't hold my breath. Because you're still wearing pajamas at 10 AM.