Just took the plunge on this offer, and this was the response: "We have received your application and further processing is required at this time. We will contact you within a week via U.S. mail regarding our decision. Thank you for requesting a Citi Executive® / AAdvantage® World EliteTM MasterCard®."
I successfully applied for the 50,000 mile Citi Business card on 11/25/13 and the 50,000 Citi platinum personal card on 1/21/14. I read somewhere on FT that if the message says you'll get a letter in a week, it means you'll be approved, and if it says you'll get a letter in 30 days it means you've been denied. It would have been nice to get approved on the spot, but this should work out OK.
Then I'll apply for my wife, but I'll wait a month or two because I'm not sure I can hit $20,000 in spending in 3 months. Hopefully, the offer will still be alive at that point.