It can takes weeks or even months to hear something, but you will eventually hear something. One time when I was working at WDW I applied for 2 better positions on the same day. One I heard from right away, got an interview, and got the job. A couple of months into my new position I got a call from the second position asking if I wanted to come in and interview. It can be crazy sometimes.
I can tell you that if you don't already work for Disney, they do give preference to existing cast members. The best advice I ever got was to go get hired for SOMETHING, ANYTHING just to get in the system and get that preference. The department you want to work for would rather hire someone that's already a CM because then they don't have to pay the cost of you going to Traditions and all the new hire costs. Also, once you're a CM you can tell your manager that you want to work for the
DCL and they are required to put you in contact with one of the managers in the department you want to work for and you can shadow which gives you a huge advantage over other applicants. At Disney they are big about promoting from within and it is part of your manager's job to help you get to where you want to go in the company.
If you're looking at a position that was posted on Disney Careers (which I'm assuming it was if it was a DCL position) then it's not "entry-level" like the ones where you just walk into casting. Every non "entry-level" role I've ever had with Disney was filled completely by existing CMs.
Disney is a great company to work for if you're willing to be a great cast member. It's great for seasonal people and it's also great to start a career.
Back to your original question, you'll just have to sit tight and wait. There's no telling how long it will be. If you are a CM or know a CM, find out who the hiring manager is for the department that you're applying for and shoot them an email, or better yet a card. All applications first get filtered out through casting using a word filter (for instance if it's a sales job they filter out applications without the word sales in the cover letter or resume) and then casting sends the rest of the applications on to the manager in charge of hiring. If you get in touch with the manager that is going through the applications, they'll at least pull yours out and look at it instead of just skimming or worse yet never even getting it which can happen (a friend of mine had his application get filtered out by casting and when he sent a card to the hiring manager they went and dug it out and he ended up getting an interview).
Good luck! Out of curiosity, what exactly was it that you were applying for? I know a lot about casting office and technical roles, but as for the actual on ship contracts for CMs to go out for months at a time, I know very little but I have some friends that do.

while you wait to hear!