Tracy,
Good news! We've found the issue. It's definitely your server time. Your time, right now, is set to:
Sun, 15 Dec 2013 18:14:12 GMT
Twitter's server is set to:
Sun, 16 Dec 2013 01:17:01 GMT
So, there's a 7 hour, 3 minute and 11s difference in your times.
I actually went into our code and added 25369 seconds to our "timestamp" and things started to work.. so, it's definitely the time.
For now, you'll have to fix the time on the server.. and, unfortunately, tweak it a bit if you can't get it right. Hopefully, you'll get it the first time.
On a side note, our JLinked extension (for LinkedIn) actually has a similar issue where the timestamp can cause issues. We have some code built-in to that to check LinkedIn's timestamp and automatically 'adjust' the value we use in case the server is off. That's worked well for JLinked, and we'll be bringing that feature over to JFBConnect in a future release as well. That helps with time drift and other oddities that can happen. We just hadn't heard of this in Twitter yet.
Please test, and let me know. If you can't get the time going, just let me know. I can check again and get you the exact time difference again as well if necessary.
Best of luck, and thanks for your patience!
Alex