I think the first thing you need to do is see if your university offers the possibility of temporarily extending your current plan after its regular coverage ends. Some schools do have this in place, and you need to contact the health plan for your school to find out if that's an option. Some schools do not extend, though, so you'll just have to find out.
If not, do a search for temporary health insurance. I needed it once, and I went with Fortis, which I believe is now Assurant Health. Anyway, it allowed me to pick exactly how many days I needed, and I don't think it was too expensive. Sure, it was much more expensive on a per day basis than any normal health plan, but considering that I only needed 42 days, or somewhere in that neighborhood, it was well worth it for my peace of mind. I think it was in the $200+ range, but I really do not remember.
Finally (and this is probably old information to you), make sure that you have the effective day of your forthcoming coverage correct. That is, some health plans don't kick in for 30 days after you begin work, so it might not necessarily start on the day that you begin working at the firm. Just thought I'd throw that out in case anyone else found it useful.
Sorry for not providing much specific advice, but bottom line is that temporary health insurance is readily available, and in my opinion, it's well worth seeking it out if you face a gap situation, even if its only a few days. You never know when you're going to need the coverage...that's the point of having insurance.