I applied for and was instantly approved for BA Chase on 4/7 for $15k. Applied for Chase Sapphire yesterday, got 'pending' message.
Today, I called up 1-888-245-0625 to check on the status and was told I'd been denied due to 'Chase card within 60 days.' I was asked why I was applying for so many cards, was honest that I have a lot of travel coming up and am trying to get miles to save money. The customer service rep agreed that it was a good idea

I offered to move some credit, suggest $6000, and was then approved. Success!!
Although I'm pleased with the outcome, I'm annoyed that the decision had clearly been made but they were waiting to deliver the news by snail mail god knows when.