It's difficult for one to turn blue and it depends on the situation. Some hypothermic patients will appear blue because of lack of blood flow, some medications when abused over time can give a person's skin a slight blue hue.
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Well, I did some research and the best I can find is less than two minutes for an adult. Since you hear about people's lips turning blue at the table, I would assume forty-five seconds to two minutes. Obviously for a child or an infant, the time would be much shorter.
If you can hold your breath that long, you'll go unconscious first and then since breathing is an involuntary event, you will start breathing again.