Last Updated Jun 21, 2010 6:15 AM EDT
There's no rule about when a start date has to be. Technically, I can make you a job offer with a start date of 2024, although why I would want to, I don't know. But, behavior such as these folks are exhibiting is not normal.
Now, if there were a really important reason why they needed you to start at the same time as another, yet to be hired person, the rational boss would say, "We're really excited about you starting with us, but the only person who is certified to teach you X, which is 90 percent of your job, lives in New Jersey, and she has to fly in for the training. To keep costs down, we're going to hold off on your start date until we've hired the second person, so that we only have to pay to fly her out once."
That makes sense, but they would have explained it to you. Actually, any rational reason would be explained. So, my guess is that these people are going to be nitpicky and controlling over things that are not important. I see this as a red flag. Sure, maybe they just hate training and want to get both new people trained together, but again, I would think they would offer you a better explanation. Telling you not to call back either indicates that you are annoying the heck out of them (which is not a good way to start) or that they are not that committed to hiring to you in the first place. It doesn't seem like they're treating this as a serious job offer.
If I were you, I'd do as requested: stop calling them and go look for another job. If this one eventually pans out, then great. But you don't want to give up potential opportunities because you have a job that will start "sometime." Not worth it.
If you are employed, don't give notice yet. If you are unemployed, don't run out and make a large purchase on your credit card in anticipation of that big fat, library assistant paycheck. Calling the HR people might spur things on, and they may be able to give you some insight into if this is normal for this particular department. However, it would also tick off the librarians who are leaving you hanging. I'd wait at least a week between your last conversation with the librarians and calling HR for clarification. After that, I don't think you have much to lose by calling.