You can check your application status online here
Barclay reconsideration line: 866-408-4064, Mon-Fri 8AM - 5PM EST.
The 24-hour number is 866-951-1437.
Based on the phone reps, an application usually remains in the system for 90 days, during which you can ask for a reconsideration.
However, if 30 days have passed, it will incur another hard pull.
There have been a few reports of Barclay pulling credit again when reconsidering - even when specifically asked not to.
Make sure to explicitly tell the rep that you don't want another credit pull. The benefit of such action would be that if later you see they did pull your credit you can call up and speak to a manager and have the pulls removed (based on first-hand accounts from this thread).
If you want to guarantee that you don't get another pull, freeze your credit report.
While Barclay recon reps are usually very tough to deal with, there have been sporadic reports of them reconsidering by reallocating credit-line from other cards. Additionally, there are a few reports indicating success with the 3BM.
Barclay recon reps take notes of each phone call and subsequent reps usually regurgitate the previous rep's reply.