They can absolutely let you go if you're not able to work nights. I'm sure you realize this by now, but schedule should have been discussed up front if you were only able to work days.
The problem is that there are likely other employees on night shift who need days for a variety of reasons. Allowing you to jump the line would be bad business and create hard feelings.
Orientation has always started on days for me, although I've always worked nights. It's less expensive because there are no differentials to pay, and new graduates tend to get more experience with admissions (and especially discharges) on day shift. There may be more senior staff available on day shift, too.
I hope everything works out for you, but I think you should start coming up with a plan "B" just in case. Ask around and see what other people you work with are doing. Maybe they'll have some good leads.