I got hired on at Spirit with less than 4000TT. I don't discount the help I got from Spirit guys here on the forums either.
It's definitely tough to get an interview but that's mainly because of the sheer amount of applications out there.
Both JetBlue and Spirit offered a class date, I chose Spirit.
My applications for US Airways, Delta and United are still out there, but as of today, haven't heard a peep, but I'm content and happy where I'm at.
The point is, don't give up. Keep your contacts going (that's the single biggest factor I believe, once you make the minimums), continue to prep and be positive. The airlines appreciate the military pilot, for their leadership, their training and their discipline, all things as a military pilot you've already proven.
Best of luck!