Seth,
First of all, Good luck on your Private Checkride! I know how your feeling right now!
Secondly, I have seen individuals not get recommended for the program. However, coming right off of a private checkride puts you into a good position for an interview with ATP. Their test in the interview has to do with (mostly) private pilot information, and your phone interview with the VP will be over your current or most recent training location, your airplane, and your airspace that you are flying in.
ATP is looking for someone with a good grasp of aviation knowlege and skill, and also someone who is open to learning. Part of your interview will be a SIM ride to see how well you take instruction. Just be professional, keep an open mind, ask questions, and be willing to learn. We can't ask for more than that...
... except for your money...
LOL!
Just relax... don't worry about ATP just yet. Let's get you through your Private first. Be sure and update the board on how it went too!
Bob