Just another data point to say that my wife and I (well, me) have been denied on Barclays card applications as well due to number of new cards/etc. I am itching to hit this card and I'll probably do an app for it during a weak moment of not wanting to wait longer but have a strong suspicion I'll be declined.
In the neighborhood of 5-8 new cards over the past year ourselves (wife and I each... (well, me)). More than sufficient income and FICO scores.