I applied two weeks ago. After 10 days, I received a letter saying I either had too much credit right now, or too much credit with Chase. I only have one card with Chase, but closed another recently. Both cards had high limits, and the one remaining still does.
I emailed to ask if they could split the credit line between the card I have and the Sapphire card. The first rep just re-sent an email copy of the same letter I had already received. The second person understood what I wanted, and said they'd forward my request to the appropriate department.
Today, I had an email approving me for the Sapphire card.