job interview by saying something along the lines of "You should hear back from us within a week or two." This is done to set expectations and to protect them from getting follow up calls too early. What do you do when those two weeks go by without any word from the employer?
The common thought when this happens is you didn't get the job. The reality is that there are many different things that can delay employers from getting back to you. Sometimes a new candidate enters the fold at the last minute, and the nonprofit wants to do its due diligence by setting up an interview. The review process could also take a lot longer if you applied to a particularly large nonprofit.
The first thing you should do if the specified time has passed is to e-mail or call the person who told you the time frame. I recommend calling, as that will give you the best chance of speaking to the person directly. Ask if they have any update on the status of your application. If they tell you it's going to take a little bit longer, ask if they have any specific time in mind. You will hopefully get a better idea of when you should be hearing back and whether you need to intensify your search for other jobs.
If you are in a position where you have received a job offer from another organization, but really want to work for the place you are waiting on, you can try and force the issue by mentioning this. If you're the candidate they really wanted, there's a possibility they may offer you the job immediately. Only use this tactic if you have been waiting a long time and need to get back to the other offer. Bluffing isn't going to get you anywhere, even if you're the best poker player in the world.