How long should I wait before I am hired after being told I had the position and it is in immediate need to be filled?

I recently moved for a job position. I was told the position was in immediate need to be filled. After being rushed and turning down two jobs, I arrived. After consistently contacting the place of employment for a week, I was finally brought in for my background check and fingerprinting. It is now been one week since I did my background check and fingerprinting. It has been 3 weeks since I've been in the state without employment. After calling and trying to get more information about the situation, I was notified that the person who does the background checks went on vacation. This means that I will be here for at least another week without employment or any sign of future employment. I do understand that background checks take some time yet they are not contacting me. I am consistently contacting them. Only to be sad story about how things are being taken care of and they clearly are not. What point should I contact someone to help me? What can be done if I am not actually offered the position?