Based on what I've seen, I doubt it matters much at all.

A credit pull dings your credit score by maybe a point or two, and it rebounds over time. I space my card applications so that I can make the minimum spends, I have never applied for two on the same day, and I have never gotten turned down (except once when Chase said I had too much credit, and then they just transferred part of my line from one card to another). I really think most people worry too much about applications and their credit scores. Now maybe if my credit score was borderline I might worry more.