At the moment, there are still many police departments struggling to find qualified people. If the economy gets worse, getting a job as a police officer (or any job) will likely become more difficult.
You should try to find out for yourself whether becoming a police officer is truly something you want to do. If you haven't see if you can do a ride-along program with a department in your area. I suggest that you consider another major. Criminal justice is a good idea, but there are many other good degrees for future police officers.
There are other jobs that a criminal justice degree would be good for such as security work, victim advocate work, corrections, other areas of the legal profession, etc.
Having only had one job wouldn't negatively affect you unless you have a negative history with that employer. Then it certainly could. Work history is something that almost anyone can improve if they want to.
Good luck, and keep us posted!