There's no set amount of time. Some people call in same day and others it takes a week or so. When my wife applied and was not instantly approved, the reps were very nice but said they could not do anything yet as the computers still had it in que. The reps are able to see your credit report and any concerns that are hanging it up. She was approved 6 days later, credit report and history were great, but having acquired two chase cards in Sept then Oct was the hold up.

Data point: She just cancelled the UA signature 7 days ago, but it wasnt even mentioned. Ironically, after she cancelled, we received a thank you for your continued signature business, and her replacement card came in the mail today. Two ships passing in the night....