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1 week.
My Venture took about 2.5 weeks.
Mine was a little different because it's secured, BUT:
I got my approval email on March 1. I got the "your card has shipped" email on March 2. I got the card in the mail on March 6 (and I know this because that's when I got my 'you've enrolled in online statements' email came in).
I was actually approved for my card a week or so before that but since it's secured it had to go through that process first.